GR20/Amaldi10 — Abstract Book

Local Organising Committee

July 6, 2013 Contents

A1 - Exact solutions and their interpretation3 Oral session...... 3 Poster session...... 12

A2 - Mathematical relativity and other progress in classical gravity theory 17 Oral session...... 17 Poster session...... 24

A3 - Modified gravity theories 35 Oral session...... 35 Poster session...... 43

A4 - Complex and conformal methods in classical and quantum gravity 51 Oral session...... 51 Poster session...... 57

B1 - Relativistic astrophysics 59 Oral session...... 59 Poster session...... 66

Joint session B2 and B4: Approximate solutions to Einstein equations, Methods and Applications’ 74 Oral session...... 74

B2 - Numerical relativity and astrophysical applications 78 Oral session...... 78 Poster session...... 86

B3 - Numerical relativity : methods, theoretical gravity and high energy applications 88 Oral session...... 88 Poster session...... 94

B4 - Analytic approximations, perturbation theory, effective field theory methods and their applications 97 Oral session...... 97

B5 - Observational cosmology 105 Oral session...... 105 Poster session...... 107

B6 - Theoretical/mathematical cosmology 110 Oral session...... 110 Poster session...... 115

C1 - Pulsar Timing Arrays: Latest Developments and Future Directions 123 Oral session...... 123 Poster session...... 127

1 C2 - GWs: Search Results, Data Analysis and Parameter Estimation 128 Oral session...... 128 Poster session...... 133

C3 - Progress and Challenges in Advanced Ground Based Detectors 145 Oral session...... 145 Poster session...... 150

C4 - Concepts and Research for Future Detectors 163 Oral session...... 163 Poster session...... 169

C5 - Space Based Detectors 178 Oral session...... 178 Poster session...... 183

C6 - Q&A Everything you wanted to know about GWs but were afraid to ask 190 Oral session...... 190

C7 - Multi-Messenger Astronomy of GW Sources 192 Oral session...... 192 Poster session...... 196

C8 - Education and Public Outreach on Gravitational Wave Astronomy 200 Oral session...... 200 Poster session...... 203

C9 - Experimental gravitation 205 Oral session...... 205 Poster session...... 214

Joint session D1, D2 and D4: The Quantum Mechanics of Black Hole Evaporation 216 Oral session...... 216

D1 - Loop quantum gravity and spin foams 218 Oral session...... 218 Poster session...... 227

D2 - Strings, branes and M-theory 229 Oral session...... 229 Poster session...... 235

D3 - Causal sets, causal dynamical triangulations, non-commutative geometry, and other approaches to quantum gravity 236 Oral session...... 236 Poster session...... 242

D4 - Quantum fields in curved space-time, semiclassical gravity, quantum gravity phe- nomenology, and analog models 243 Oral session...... 243 Poster session...... 254

2 A1 - Exact solutions and their interpretation

Oral session

Sagemanifolds: a free package for differential geometry and tensor calculus

Gourgoulhon E, Bejger M

SageManifolds is a new package for the modern computer algebra system Sage, implementing differential geometry and tensor calculus. As Sage, it is a free and open source software based on the Python pro- gramming language. This last feature makes it easy to use for anybody with a basic knowledge of Python. We shall present SageManifolds, focussing on applications to general relativity, such as computations of the Riemann and Ricci tensors in spacetimes of arbitrary dimensions, performing complicated changes of coordinates, evaluating the intrinsic and extrinsic geometry of submanifolds, performing conformal decompositions, using exterior calculus on differential forms, checking exact solutions of Einstein equa- tions and visualization of tensorial fields. Computationally-heavy tasks may be assisted using Cython, the C-extensions for the Python language, to improve the overall speed. We shall also demonstrate the pedagogical usage of SageManifolds in teaching general relativity.

Analyzing and visualizing the kerr vacuum via gradient flows

Abdelqader M , Lake K

We explore the global structure of the Kerr spacetime using a new visualization and analysis tool based on gradient fields of scalar invariants. We discover that the observable structure (i.e. outside the horizon) of the Kerr vacuum does not vary smoothly with the spin parameter, but goes through a significant qualitative change at some specific ”transitional” values of the spin parameter. The number of the gradient fields’ critical points and their index, or winding number, along the axis of symmetry changes at these transitional values of angular momentum. This result is more than a mathematical exercise, since these gradient fields represent the cumulative tidal and frame-dragging effects of the spacetime in an observer independent way. Therefore, the result has significant applications in theoretical astrophysics by possibly providing an alternative method to extract mass and angular momentum information in numerical relativity simulations, as well as shedding light on the effect of different spin parameter values on the characteristics of relativist jets produced by black holes.

3 Regularized kerr-newman solution as a model of spinning particle

Burinskii A

Parameters of spinning particles correspond to over-rotating Kerr geometry, for which the black-hole horizons disappear and the Kerr singular ring is naked, forming a two-sheeted Kerr-Schild background, which requires formation of a regular source. We discuss development of the regular model of the source of Kerr-Newman (KN) solution from the Keres-Israel-Hamity rotating disk model to the L’opez membrane-bubble model, and further to the gravitating soliton model, which is formed as a domain wall bubble, representing a bag filled by Higgs field in a false-vacuum state [arXiv: 1003.2928]. We describe a supersymmetric model of the corresponding phase transition. The gravitating soliton model of the KN source has important peculiarities: 1) the internal Higgs field is oscillating with frequency ω = 2m, 2) there appears the vortex-like closed superconducting string, 3) the KN vector potential forms a closed Wilson loop, which requires quantizatio

Scalar multi-wormholes

Sushkov S, Egorov A, Kashargin P

We construct an exact axially symmetric solution describing n wormholes in general relativity with the phantom scalar field possessing the negative kinetic energy. The spacetime of multi-wormholes is everywhere regular and has no event horizons. It has a complicated topological structure. Namely, in the spacetime there exist 2n asymptotically flat regions connected by throats.

Off-diagonal wormhole deformations in modified massive gravity

Vacaru S

There are explored off-diagonal deformations of ”prime” metrics in Einstein gravity (as examples, we cosider wormhole configurations) into ”target” exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be char- acterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in par- ticular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that the solutions with nontrivial nonholo- nomically induced torsion can not be alternatively described as effective/analogous Einstein spaces. For zero torsion configurations, there are nonholonomic tansforms and/or non-trivial limits to exact solu- tions in general relativity when modified/ massive gravity effects are modelled by off-diagonal and/or nonholonomic parametric interactions.

Static spherical black holes with scalar field

Tafel J

We describe static spherically symmetric black holes with a self-interacting scalar field in terms of one function which satisfies simple conditions. We analyze global structure of solutions and admissible potentials of the scalar field. Then we apply this approach to asymptotically anti-de Sitter spacetimes and particle-like nonsingular field congurations. We present numerical examples of solutions.

4 Relativistic charged spheres: exact solutions for stars, regular black holes and quasiblack holes

Lemos J , Zanchin V

Guilfoyle [1] found a class of exact solutions of spherically symmetric distributions of charged matter matched smoothly to a Reissner-Nordstrom solution, in which the interior parameters are given uniquely in terms of the exterior global ADM mass and electric charge and have several interesting properties [2]. Here we show that this class of solutions hides a rich variety of bodies and spacetimes. Indeed, one finds undercharged, extremal charged and overcharged stars, regular black holes, and quasiblack holes, these latter may even be considered the real frozen stars [3], i.e., collapsed compact stars with their boundary surfaces looming at their own gravitational radii. The spectrum of solutions also contain bridge spacetimes with negative electromagnetic field energy of the type considered by Einstein and Rosen to mimic an electron as a nonsingular particle solution of the theory [4]. The charged solutions yield appropriately the Andreasson limit [5] which in turn gives the Buchdahl limit in the uncharged case. [1] S. Guilfoyle, Gen. Relativ. Gravit. 31, 1645 (1999); arXiv:gr-qc/9906089. [2] J. P. S. Lemos, V. T. Zanchin, Phys. Rev. D 80, 024010 (2009); arXiv:1004.3574 [gr-qc]. [3] J. P. S. Lemos, V. T. Zanchin, Phys. Rev. D 81, 124016 (2010); arXiv:0905.3553 [gr-qc]. [4] A. Einstein, N. Rosen, Phys. Rev. 48, 73 (1935). [5]. H. Andreasson, Commun. Math. Phys. 288, 715 (2009); arXiv:0804.1882 [gr-qc].

The conformal cousin of the husain-martinez-nunez spacetime

Faraoni V

A 2-parameter inhomogeneous cosmology of Brans-Dicke theory, obtained by conformally transforming the Husain-Martinez-Nunez scalar field solution of the Einstein equations is studied. According to the values of the parameters, it describes a wormhole or a naked singularity. The reasons why there isn’t a one-to-one correspondence between conformal copies of this metric are discussed.

Deformations of black holes in external gravitational fields

G¨urlebeck N

The deformation of neutron stars and black holes due to external gravitational fields is characterized by the first and second Love numbers in Newtonian gravity. They measure the deformation of the surface and the induced multipole moment caused by a specific external field. Analogous definitions were employed in General Relativity, e.g., in [T. Damour & O. M. Lecian, PRD, 80,044017 (2009); T. Binnington & E. Poisson, PRD, 80, 084018 (2009)]. However, these approaches require necessarily linearization and approximations. With these approximations, it was established that the second Love numbers of static black holes vanish. Is this still true if higher non-linear effects are taken into account? In this talk, I employ the source integrals for asymptotic multipole moments of [N. G¨urlebeck, gr- qc/arXiv:1207.4500] to show analytically without any perturbation scheme that the induced multipole moments and, thus, the second Love numbers of static black holes vanish. Thereby, I corroborate the existing results without resorting to any approximations. This implies that the contributions of the dis- torted black hole to the asymptotic multipole moments are exactly those of an undistorted Schwarzschild black hole. This can be seen as a generalization of the no-hair theorem if additional matter is present. Nonetheless, the internal geometry of the horizon changes, which is characterized by the first Love numbers.

5 Dynamics of black holes in ads2 x s2 spacetimes (bertotti-robinson universes)

Alekseev G

Using the monodromy transform approach and corresponding linear singular integral equation form of the symmetry reduced Einstein - Maxwell equations, we construct in a very simple form the exact solutions of these equations which describe (a) Schwarzschild black hole at static position in Bertotti-Robinson magnetic universe; (b) Schwarzschild black hole in arbitrary “geodesic” motion along the magnetic field in the Bertotti-Robinson pure magnetic universe; (c) Reissner-Nordstrom black hole accelerated by the electric field of the Bertotti-Robinson pure electric universe. In each of these cases, we have in an explicit form a picture of a nonlinear interaction of gravitational and electromagnetic fields of a black hole with those of the Bertotti-Robinson universe which are (in the absence of a black hole) static and spatially homogeneous. In all cases, the character of motion (and in particular, the acceleration) of a black hole is determined by the condition of absence of conical singularities on both parts of the axis of symmetry outside the horizon. This condition imposed on the parameters of the solution relates the acceleration of a black hole with the values of its charge and of the external electric field (the analogue of the Lorenz force). Various physical and geometrical properties of these solutions are described.

Black holes in 4-dimensional supergravity

Chow D

I shall present some new black hole solutions of 4-dimensional supergravity. These will include both asymptotically flat solutions in ungauged supergravity and asymptotically anti-de Sitter solutions in gauged supergravity, in particular solutions of N=8 supergravity. The solutions can have multiple electric and magnetic charges, and some examples are rotating. In general, they have a non-zero temperature, but include examples that are extremal and supersymmetric. I shall discuss the solution generating technique for finding the solutions of ungauged supergravity, involving Kaluza-Klein reduction to a coset model in 3 dimensions. I shall comment on the thermodynamical properties of the solutions and geometrical properties.

Black rings in higher dimensions

Kleihaus B, Kunz J , Radu E

Discovered by Emparan and Reall, black rings received much attention in recent years. Exact analytic black ring solutions are known in five dimensions. In more than five dimensions no general analytic framework for their construction is known. Therefore we have resorted to numerical techniques to solve the Einstein equations and learn about the properties of black rings in more than five dimensions. We have constructed a family of balanced black rings in six dimensions, that allows us to obtain most of the phase diagram for these objects. In particular, we have found two branches of black rings. For large ring radii, analytic perturbative results obtained within the blackfold approach are available. Our branch of thin black rings agrees well with these results within their range of validity. However, we have also found a branch of fat black rings, which extends towards a horizon topology changing solution, where it is expected to merge with a branch of pinched black holes.

6 Maximal slices of five-dimensional black holes

Kunduri H

The constant-Boyer-Lindquist time slices of the Kerr spacetime represent asymptotically flat, maximal spacelike hypersurfaces (i.e. vanishing trace of the extrinsic curvature) with topology RXS2. I will discuss some aspects of the geometry and topology of maximal slices of various stationary black hole solutions of the vacuum Einstein equations in five dimensions. These slices are complete asymptotically flat Riemannian manifolds with inner boundaries (minimal surfaces) corresponding to the black hole horizon. Although these spaces are simply connected, they can have non-trivial topology. As much of the analysis is at the topological level, we can also consider slices of black holes for which explicit geometries are not yet known. In particular, we can compute the homology groups for a large class of such slices.

Algebraic classification of kundt geometries in four and higher dimensions

Podolsky J , Svarc R

We present a complete classification of general Kundt class of spacetimes in arbitrary dimension for which the non-expanding, non-twisting, shear-free null direction is a (multiple) WAND. No field equations are used, so that the results apply not only to Einstein’s gravity and its extension to higher dimensions, but also to any metric theory of gravity which admits the Kundt spacetimes. By an explicit evaluation of the Weyl tensor in a natural null frame we demonstrate that all Kundt geometries are of type I, and we derive simple necessary and sufficient conditions under which the optically privileged direction becomes double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, IIi, IIIi, D(a), D(b), D(c) and D(d). The conditions are surprisingly clear and expressed in an invariant form. Some of them are always satisfied in four dimensions. To illustrate our classification scheme, we apply it to several important subfamilies of the Kundt class, namely the pp-waves, the VSI spacetimes, and generalization of the Bertotti-Robinson, Nariai, and Plebanski-Hacyan direct-product spacetimes of any dimension. For more details see arXiv:1303.0215 [gr-qc].

Geometric optics of algebraically special spacetimes in higher dimensions

Ortaggio M , Pravda V, Pravdova A

The standard form of the four-dimensional Goldberg-Sachs theorem does not admit a straightforward extension to higher dimensions (as demonstrated, e.g., by the rotating black hole metric of Myers and Perry). However, in the past few years several constraints on the optical properties of null congruences “aligned” with the Weyl tensor (WANDs) have been obtained. Here we summarize main results that extend the “shearfree” part of Goldberg-Sachs theorem to Einstein spacetimes in six and higher dimen- sions, which requires several special cases to be discussed separately. The geometrical meaning of our results in terms of integrability properties of certain totally null distributions will also be mentioned, and some explicit examples of spacetimes with multiple WANDs with various properties will be presented.

Higher dimensional gravitating fluids

Nyonyi Y , Maharaj S, Govinder K

We study shear-free spherically symmetric cosmological models with heat flow and charge defined on

7 an (N + 2)−dimensional manifold. We analyse the pressure isotropy condition, a highly nonlinear partial differential equation (which we can treat as an ODE), using Lie’s group theoretic approach. The symmetry generators that leave the equation invariant are found. We provide exact solutions to the gravitational potentials using the first symmetry admitted by the equation. Our new exact solutions contain the earlier results without charge. Using the remaining symmetries we are able to provide other solutions or reduce the order of the master equation to a first order nonlinear differential equation.

Conformal structure of past and future end states of frw models with scale factors of generalised power series form

Scott S, Threlfall P

It has been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A promising school of thought for its explanation is quiescent cosmology which already possesses a mathematical framework, namely the definition of an isotropic singularity, but only for the initial state of the universe. A complementary framework was necessary to also describe possible final states of the universe. In 2009 Hoehn and Scott formulated new definitions of an anisotropic future endless universe and an anisotropic future singularity, whose structure and properties differ significantly from those of the isotropic singularity, offering a promising realisation for this framework. Using this framework, we consider the past and future end states of Friedmann-Robertson-Walker (FRW) space-times with a scale factor expressed as a generalised power series. There has been considerable interest in the different types of singularities that the FRW space-times admit, namely Big Bangs, Big Crunches, Big Rips, Sudden Singularities and Extremality Events. We present a discussion and comparison of these singularities in relation to the generic conformal sin- gularities defined by Hoehn and Scott; the Isotropic Past Singularity (IPS), Isotropic Future Singularity (IFS) and Future Isotropic Universe (FIU).

An exact smooth gowdy-symmetric generalized taub-nut solution

Hennig J

”Smooth Gowdy-symmetric generalized Taub-NUT solutions” are a class of inhomogeneous cosmolog- ical models with spatial S3-topology. In this talk, we derive and discuss a three-parametric family of exact solutions within this class, which contains the two-parametric Taub solution as a special case. In particular, we show that, for a special choice of the parameters, the spacetime contains a curvature singularity with directional behaviour. For other parameter choices, the maximal globally hyperbolic region is singularity-free.

8 New spherically symmetric solutions for spherical objects with charge and anisotropic pressures

Raghoonundun A, Hobill D

A large number of solutions to the static and spherically symmetric Einstein Field Equations (EFE) in the presence of matter exist. However numerous reviews show that even under the simplifying assumptions of matter isotropy and charge neutrality, less than 10% of these solutions have properties that are physically realistic. We have searched for new solutions that forgo the above two simplifications, but at the same time behave physically. These new solutions are based on the method Tolman used to find the physically realistic Tolman VII (T7) solution. The T7 method was crucial because of the form of the final differential equation resulting from the T7 density ansatz. The two new exact solutions found (one incorporating anisotropy, the other both charge and anisotropy) obey well-known conditions for physical acceptability for some parameter ranges. Since we are solving the EFE directly, an equation of state (EOS) relating energy density and fluid pressure is obtained as a by-product of these solutions.

Magnetized axially symmetric thin dust disks in conformastatic spacetimes

Gonzalez G

An infinite family of new solutions of the Einstein-Maxwell equations for axially symmetric confor- mastatic spacetimes is presented. This family of solutions describe thin dust disks made of material sources with a surface conduction current. The solutions are obtained by expressing the metric function and the magnetic potential in terms of an auxiliary function which satisfies the Laplace equation, a characteristic property of the conformastatic spacetimes. By introducing then a finite discontinuity on the first derivatives of the metric tensor, solutions with a delta function type singularity with support on the hypersurface z = 0 are obtained, describing so infinitesimally thin disks of infinite extension. Then, the surface energy-momentum and the surface current density of the disk are obtained by using the formalism of tensorial distributions and their physical content is analyzed. A simple particular model is presented in which the energy is well behaved everywhere and the energy-momentum tensor satisfies all the energy conditions. Furthermore, although the thin disks are of infinite extension, their total mass is finite.

Splitting thin shells and the evolution of distributional solutions of einstein equations

Ramirez M

In this talk we study the existence of exact solutions that represent thin shells that at a point of their evolution split into a number of different shells in a differentiable manner, and of solutions that represent thin shells that acquire thickness as a result of the evaporation of some of their constituents. These constructions are fairly natural as they arise from stability analyses under infinitesimal separations of non-interacting shell constituents. In this way, their existence compromises the uniqueness of the evolution of thin shell models. We then analyze some conceptual issues associated with the initial value problem for distributional solutions of hyperbolic PDE systems, particularize to the case of thin shells in GR, and propose a mathematical framework in which the IVP might be defined and analyzed.

9 Spinning test particle trajectories in de sitter spacetime

Cole R, Gair J, Babak S

It is well-known that unstructured test particles in General Relativity follow geodesic trajectories in the background spacetime. This is the leading order result from a multipolar expansion of the energy- momentum tensor of the test body. At next order, including pole and dipole terms, the Mathisson- Papapetrou (MP) equations of motion for spinning test particles are recovered. In addition, a Spin Supplementary Condition (SSC) must be specified to fix the worldline of the body. We present an analytic solution to the MP equations in de Sitter spacetime using the Frenkel-Pirani SSC and the w- condition. We discuss methods of studying the motion of spinning test particles in black hole spacetimes, using the de Sitter solution to gain insight into the problem. This has applications in the generation of waveform templates for extreme-mass-ratio inspirals, which consist of a stellar mass compact object in orbit around a supermassive companion. The gravitational waves emitted by such a system are expected to be below the level of noise in a detector and so to extract the waveform from the data using matched filtering, a bank of templates covering the parameter space needs to be produced. The presence of spin in the compact object can lead to a significant dephasing over the lifetime of the inspiral and so it is important to include its effect in waveform templates.

Gravitational lensing by gravitational waves

Harte A

Gravitational lensing has been an integral part of general relativity from its very beginning. Since that time, the subject has developed to a very high degree of sophistication both theoretically and observa- tionally. Nevertheless, much of the work on the subject has focused on lensing in stationary systems. In this talk, I discuss lensing by (decidedly non-stationary) gravitational waves. Assuming planar symmetry, various results can be computed exactly. Images of objects are typically distorted, change brightness and color, and appear to move across an observer’s sky due to the presence of gravitational waves. Multiple images can also be formed. Even in the simplest cases involving short wavepackets, extremely dramatic effects occur generically. Essentially any observer in such a spacetime eventually reaches a point in time at which light from the entire universe is momentarily concentrated to a single point in the sky. Formally, this light is infinitely blueshifted and was emitted in the infinitely distant past. Later, the contributions to this flash from different sources appear to separate from each other, dim, and then redshift away.

Gravitational deflection of light ray in plasma

Tsupko O, Bisnovatyi-Kogan G

We consider the gravitational deflection of light rays in plasma and gravitational lensing in plasma. We have found, that in absence of refraction, in a homogeneous dispersive medium, the gravitational deflection is qualitatively different from the vacuum case, and the deflection angle depends on the photon frequency. We have obtained for the first time a simple analytical formula for the light deflection in a Schwarzschild metric, in presence of a homogeneous plasma. The deflection angle depends on the photon frequency, what resembles the properties of the refractive prism spectrometer. The effect of difference from the vacuum case in the gravitational deflection angles is significant only for the radio waves. Using these results, we develop a model of gravitational lensing in plasma. The observational effect of the frequency dependence may be demonstrated on the example of the Schwarzschild point-mass lens. Instead of two point-like images with complicated spectra, we will have two line images, formed by the photons with different frequencies, which are deflected by different angles. We developed also a more

10 general approach, considering an inhomogeneous plasma, where a non-gravitating refractive deflection is also taken into account. So called relativistic images in a homogeneous plasma, which are formed by the photons performing one or several revolutions around the central object, are also investigated in details.

Observational features of perfect fluid sources with a singularity at the center

Malafarina D

We consider a perfect fluid interior solution to the Schwarzschild metric belonging to the class inves- tigated by Tolman. We show how such a configuration can be achieved dynamically via gravitational collapse. Assuming that the cloud is optically thin and surrounded by an accretion disk we evaluate its observational properties in order to determine whether such sources could in principle be distinguished from a black hole of the same mass.

Point massive particle in general relativity

Katanaev M

It is well known that the Schwarzschild solution describes the gravitational field outside compact spher- ically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein’s equations with δ-type source corresponding to a point particle is not known. We prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric and geodesically complete solution of Einstein’s equations with δ-type energy-momentum tensor corresponding to a point particle. Solution of Einstein’s equations is understood in the generalized sense after integration with a test func- tion. Metric components are locally summable functions for which nonlinear Einstein’s equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighbourhood.

11 Poster session

Generalized ltb solution

Koptyeva E, Korkina M

An interest for studying generalizations for LTB-solutions arises from consideration of local groups be- havior on the background of cosmological expansion. These types of solution are also useful in the study of black hole dynamical horizons, black hole thermodynamics and also of primordial black holes as probes of the early universe. This issue has received much attention over the years, however, these discussions produced contradictory results leaving the problem unsolved. In this work we use so called ”mass function method” and build the consistent exactly solvable model of Schwarzschild black hole in the universe filled with dust-like matter.

Matching of the de sitter solution and solution for anisotropy perfect fluid

Korkina M, Iegurnov O

The matching of spherically symmetric de Sitter solution and shear-free solution for homogeneous anisotropy perfect fluid was examined. The matching was realized by Lihnerovich-Darmua conditions on the hypersurface t = constant (where t is the time of perfect fluid solution). The conditions of matching on this hypersurface were obtained. From this conditions follows equality of the energy density on the considered hypersurface for both metrics. The fact, that between above solutions exist matchig and from the matching conditions follows energy density equality makes combination of these solution interesting for the constructing cosmological models and models of the physical objects.

Axially symmetric relativistic thin disks immersed in spheroidal matter haloes

Gonz´alezVillegas G, Pimentel D´ıazO

An infinite family of axially symmetric relativistic thin disks of dust immersed in spheroidal matter haloes is presented. The disks are obtained from solutions of the Einstein equations for an axially symmetric conformastatic spacetime in which the metric tensor is characterized only by one metric function. By introducing a finite discontinuity on the first derivatives of the metric tensor, solutions with a singularity of the delta function type are obtained, so that they describe infinite thin disks. The nonzero components of the energy-momentum tensor, both for the disk and the halo, are obtained from the Einstein equations. In this way, the energy densities and pressures of the sources are determined. By imposing the fulfillment of all the energy conditions we obtain a constraint over the solutions, in such a way that the metric function can be properly expressed in terms of a solution of the Laplace equation. A simple particular example is presented with energy densities and pressures well behaved everywhere. Furthermore, although the disks and the haloes are of infinite extension, their masses are finites.

12 Relativistic static thin disks with electrically and magnetically polarized material source

Gonzalez G, Navarro A

An infinite family of relativistic static thin disks with electrically and magnetically polarized material source is presented. The solutions are obtained by considering the Einstein-Maxwell equations for contin- uum media in a conformastatic spacetime so that the metric function and the electromagnetic potential can be properly expressed in terms of an auxiliary function solution of the Laplace equation. Then, given a complete solution of the Einstein-Maxwell equations, a finite discontinuity of the first derivatives of the metric tensor is introduced in order to have a solution with a singularity of the delta function type which can be interpreted as an infinite thin disk. Using then the formalism of tensorial distributions, the energy-momentum tensor of the source is obtained and its physical content is analyzed by determining the behavior of the surface energy density, the radial and azimuthal stresses, as well as the components of the electromagnetic field and the surface polarization and magnetization. Finally, a simple example is considered where the all physical quantities are everywhere well behaved, and the energy-momentum tensor of the source is in fully agreement with the complete energy conditions.

Anisotropic charged exact models

Sunzu J

New exact solutions for the Einstein-Maxwell equations are found. This class of solutions is obtained by considering the anisotropic charged stars. We include the linear equation of state consistent with quark stars. The master differential equation is integrated after specifying the measure of anisotropy and one of the gravitational potentials which are physically reasonable. We present new anisotropic solutions which are non-singular at the center through which we regain isotropic results. Graphical and physical analysis of the results are presented.

Some polytropic solutions in general relativity

Mafa Takisa P

The Einstein-Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43: 1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44: 1419, 2012) are recovered. We also obtained exact solutions for neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the radial pressure profiles are consistent with earlier treatment which suggest relevance in describing relativistic compact stars.

13 Some polytropic solutions in general relativity

Mafa Takisa P

The Einstein-Maxwell equations with anisotropic pressures and electro- magnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43: 1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44: 1419, 2012) are re- covered. We also obtained exact solutions for neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the ra- dial pressure profiles are consistent with earlier treatment which suggest relevance in describing relativistic compact stars.

Lie symmetries for a radiating star in conformally flat spacetime

Abebe G, Govinder K, Maharaj S

We study the junction condition for a shear-free radiating spherically symmetric relativistic star when the Weyl tensor vanishes and there are no tidal effects. We transform the governing nonlinear partial differential equation to ordinary differential equations using the method of Lie analysis. Particular solutions to the transformed equation are presented.

Exact interior solutions in einstein-gauss-bonnet gravity

Chilambwe B, Hansraj S, Maharaj S

While the general theory of relativity proposed by Einstein continues to be the most successful theory of the gravitational field, it does come short in explaining certain observed phenomena such as the late time expansion of the universe. One approach to correct this deficiency is to allow the action principle to include more than just linear forms of the Riemann and Ricci tensor as well as the Ricci scalar. In this regard the Lovelock (1971) polynomial and its simpler version the Gauss-Bonnet Lagrangian is useful. We seek to find new exact interior models for 5D Einstein-Gauss-Bonnet (EGB) theory in the case of a spherical distribution of perfect fluid. When the higher order effects are switched off, regular Einstein field equations are regained. To our knowledge such exact solutions have not been found, the case of dust (zero pressure) (Ghosh and Maharaj 2012), constant density sphere (Dadhich, et al 2010) and collapse in 5D EGB theory has been studied . It should be noted that the exterior of a 5D sphere in EGB theory is given by the Boulware and Deser metric (1985). We express the 5D EGB field equations in the standard canonical coordinates and then introduce a coordinate transformation which allows the single master field equation to be expressible as a second order ordinary differential equation in one of the gravitational potentials. We then make a choice for the remaining gravitational potential that allows the master field equation to be integrated and analysed.

Spherically symmetric solution of gravitation theory with deser-dirac scalar field in riemann-weyl space

Frolov B, Febres E

As a result of the Poincar’e-Weyl gauge theory of gravity, space-time is endowed with a geometric structure of the Cartan-Weyl space with curvature, torsion and nonmetricity of the Weyl’s type, as

14 well as an additional geometric structure in the form of the scalar Deser-Dirac field. If torsion is zero, this space is called the Riemann-Weyl space. In the frame this approach, the conformal theory of the gravitational field was constructed and the field equations were derived in the formalism of the external forms. For the central (nonrotational) mass m the solution for the metric and the scalar field is Yilmaz- Rosen metric. This metric first emerged in the original theory of gravitation of Yilmaz, in which it was postulated that the metric of a Riemann space is a special function of the scalar field. The interest in this metric aroused by the fact that this metric has no singularity, which is characteristic for the Schwarzschild metric, and does not describe a black hole type solution, but at large distances coincides with the Schwarzschild metric. Therefore existence of the Deser-Dirac scalar field, which is essential, because it has a fundamental, as well as the metric, geometrical status. Under certain circumstances it can modify the black hole metric at short distances. Also there is a possible essential role of the Deser-Dirac field on extremely short distances, which can be manifested, for example, in the fate of the final stage of the collapse of massive stars.

Cosmological solution for the early universe in a cartan-weyl space with the deser-dirac scalar field

Lipkin K , Babourova O, Frolov B

Post-Rimannian spaces allocated such geometrical structures as curvature, torsion and nonmetricity have now the increasing value in the classical theory of gravitation. On the basis of the Poincar´e–Weyl gauge theory of gravitation [1] it has been shown, that a geometrical spacetime background is the geometrical structure of Cartan–Weyl space CW4 with a curvature gabQ. Also it has been shown, that in the framework of the gauge procedure developed in [1], in a natural way, as an additional geometrical variable there emerges a scalar field with the properties of the scalar field entered by Dirac [2] and earlier by Deser [3]. Developing the given approach, the conformal theory of gravitational field has been constructed in [4]–[7] and the field equations of the theory have been deduced in a formalism of external forms [6], [7] (is the Einstein cosmological constant).

Algorithms generating new models

Ngubelanga S, Maharaj S, Ray S

We study spherically symmetric spacetimes related to the Einstein field equations. We generate new exact solutions to the field equations with isotropic pressures. The condition of pressure isotropy is expressed as a linear equation. An algorithm is developed that produces a new solution if a particular solution is known. There are fundamentally new classes of solutions to the condition of pressure isotropy.

On the goldberg-sachs theorem in five dimensions

Pravda V

We discuss a generalization of the Goldberg-Sachs theorem to the case of five-dimensional Einstein spacetimes. While in full generality the optical matrix has six free parameters, the algebraically special property restricts the optical matrix to one of three canonical forms involving just two free parameters. Explicit examples of exact five-dimensional solutions corresponding to each form will be given.

15 Matching of the de sitter solution and solution for perfect fluid with nonuniform pressure

Korkina M, Iegurnov O

The matching of spherically symmetric de Sitter solution and shear-free solution for perfect fluid with uniform density but with nonuniform pressure was examined. The matching was realized by Lihnerovich- Darmua conditions on the hypersurface t = constant (where t is the time of perfect fluid solution). The conditions of matching on this hypersurface were obtained. From this conditions follows equality of the energy density on the considered hypersurface for both metrics. The fact, that between above solutions exist matchig and from the matching conditions follows energy density equality makes combination of these solution interesting for the constructing cosmological models and models of the physical objects.

The gravitational field of a relativistic sphere of incompressible liquid and ”gauge” freedom.

Kozyrev S

We present the new class of relativistic static spherically symmetric configuration of incompressible liquid. This class of configurations is obtained by considering only a spherical arithmetization of manifold. The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. ”Gauge” fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric generated by static spherically symmetric distribution of matter can be matched with wide family of vacuum solution and the exterior spacetime geometry could not be deduced directly from the interior perfect fluid solution, without reference to a ”gauge” fixing or vice versa. The property of solutions in general relativity is indeed an observer dependent concept.

Killing vector analysis in ghp formalism of conformally flat pure radiation metrics with negative cosmological constant

Bradley M , Machado Ramos M

In a paper by Edgar and Ludwig it was shown how the symmetry analysis of a spacetime may be considerably simplified when using intrinsic GHP tetrads. A generalised Lie derivative operator, that reduces to the usual Lie derivative when acting on zero-weighted quantities, was introduced. The Killing equations are then obtained by acting with the commutators of this derivative and the GHP operators on zero-weighted scalars (the intrinsic coordinates). In this work we extend the method to a class of spacetimes with null rotation isotropy, where an intrinsic GHP tetrad cannot be completly found. The Killing vectors of the conformally flat pure radiation metrics with negative cosmological constant are then determined and the result is compared with other methods.

16 A2 - Mathematical relativity and other progress in classical gravity theory

Oral session

Rotating, stationary, axially symmetric spacetimes with collisionless matter

Andreasson H

I will present a result on the existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum. This provides models for rotating asymptotically flat spacetimes with collisionles matter. If angular momentum is allowed to be non-zero, the system of equations contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled efficiently by recasting the equation as one for an axisymmetric unknown on R5. This is a joint work with Markus Kunze and Gerhard Rein.

A covariant action principle for dissipative fluid dynamics

Andersson N

In this talk I will present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are i) the use of a lower dimensional matter space for each fluid component, and ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism will be developed in several steps and the model example of matter coupled to heat is considered at each level. Thus, I will discuss a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. The new formalism impacts on both applications and foundational issues.

The resolution of the bounded l2 curvature conjecture in general relativity

Szeftel J

In order to control locally a space-time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 curvature conjecture roughly

17 asserts that one should only need L2 bound on the curvature tensor on a given space-like hypersuface. This conjecture has its roots in the remarkable developments of the last twenty years centered around the issue of optimal well-posedness for nonlinear wave equations. In this context, a corresponding conjecture for nonlinear wave equations cannot hold, unless the nonlinearity has a very special nonlinear structure. I will present the proof of this conjecture, which sheds light on the specific nonlinear structure of the Einstein equations. This is joint work with S. Klainerman and I. Rodnianski.

Propagation and interaction of impulsive gravitational waves

Luk J , Rodnianski I

We initiate the rigorous mathematical study of the propagation and interaction of impulsive gravita- tional waves. The problem is studied in the context of a characteristic initial value problem with data given on two null hypersurfaces and containing curvature delta singularities. We establish an existence and uniqueness result for the spacetime arising from such data. In the spacetime, the curvature delta singularities propagate along 3-dimensional null hypersurfaces germinating from the initial singularities and the spacetime remains smooth away from these hypersurfaces. The construction of these spacetimes is motivated in part by the celebrated explicit solutions of Penrose, Khan-Penrose and Szekeres. In this talk, we will also compare the impulsive gravitational spacetimes with null singularities conjectured to be generic in the interior of black holes.

Extremal black holes with regular interior in einstein-yang-mills-higgs theories

Breitenlohner P, Forgacs P, Maison D

Families of static, spherically symmetric asymptotically flat, extremal black hole solutions with regular interiors are constructed in an SU(2) Einstein-Yang-Mills-Higgs theory. It is shown by combining an- alytical and numerical methods that there are two types of such magnetically charged extremal black holes, either with Abelian exteriors (extremal Reissner-Nordstrom solution) or with nonabelian hair. Although these solutions are non-analytic at the horizon, there exist solutions being at least twice dif- ferentiable there. Also freely falling observers do not necessarily experience infinite tidal forces when crossing the horizon. This work completes previous results by Breitenlohner, Forgacs, Maison and by Lue and Weinberg on non-abelian black hole-monopoles.

Analyticity of event horizons of extremal kaluza-klein black holes

Kimura M

Abstract: We discuss the analyticity of event horizons of extremal Kaluza-Klein black holes. We show that the metrics admit C1 extension across the horizon, but some component of Riemann tensor measured by a free fall observer is always diverge at the horizon if the space time dimensions is higher than 6 unlike the case of five dimension where the event horizon is analytic. The singularity is relatively mild so that an observer along a free-fall geodesic can traverse the horizon. We also discuss the case of space times with a twisted extra dimension.

18 What happens at the horizon of an extreme black hole?

Reall H

Aretakis has demonstrated the existence of an instability of a massless scalar field at the horizon of an extreme Reissner-Nordstrom or extreme Kerr black hole. After reviewing this discovery, I will explain how this result can be generalized to any extreme black hole, and that a corresponding instability occurs for linearized electromagnetic and gravitational perturbations. I will then discuss the results of numerical simulations which demonstrate that this instability persists when the gravitational backreaction of the scalar field is included. This talk is based on joint work with J. Lucietti, K. Murata and N. Tanahashi.

Uniqueness of extreme horizons in einstein-yang-mills theory

Lucietti J

It is well known that the black hole uniqueness theorem fails in Einstein-Yang-Mills theory. Nevertheless, I will show that in this theory any stationary and axisymmetric black hole with a degenerate horizon, must have the near-horizon geometry of an abelian embedded extreme Kerr-Newman black hole. I will also show that the near-horizon geometry of any static degenerate black hole is the direct product AdS(2) × S2. Analogous results are presented with the addition of a cosmological constant.

Construction of dynamical vacuum black holes

Holzegel G

[joint work with M.Dafermos and Igor Rodnianski] We prove the existence of a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotes in time to a fixed Schwarzschild or Kerr metric. The spacetimes are constructed by solving a backwards scattering problem for the vacuum Einstein equations with characteristic data prescribed on the event horizon and (in the limit) at null-infinity. Being parametrized by scattering data, the class admits the full functional degrees of freedom to specify data for the Einstein equations. An essential feature of the construction is that the solutions converge to stationarity exponentially fast, with their rate of decay being intimately related to the surface gravity of the event horizon. This can be traced back to the celebrated redshift effect, which in the context of the above scattering problem is seen as a blue shift.

Generalization of initial data for the kerr metric

Tafel J

We generalize initial data induced by the Kerr metric on hypersurfaces t=const. Considered data cor- respond to axially symmetric nonstationary (in general) 4-dimensional metrics. Initial metic is not conformally flat and the exterior curvature tensor has very simple algebraic structure. The momentum constraints are explicitly solved and the Hamiltonian constraint is proved to have unique solution within the York conformal method. The class of data admits arbitrary functions of 2 variables. A construction of asymptotically flat data containing marginally trapped surfaces is presented.

19 Almost birkhoff theorem in general relativity

Goswami R, Ellis G

We extend Birkhoff’s theorem for almost LRS-II and almost vacuum spacetimes to show the rigidity of spherical vacuum solutions of Einstein’s field equations continues even in the perturbed scenario.

A study of the field equations in the neighborhood of a solitary black hole.

Perez A, Kozameh C , Moreschi O, Gallo E

In this work we present a construction that provides a framework for the study of gravitational collapse of an isolated system in its late stage of evolution. We first define a family of spacetimes representing non-stationary black holes exhibiting remarkable universal properties which are natural generalizations from stationary spacetime. We then give characteristic data on the event horizon and on null infinity together with conditions on the gravitational falloff near timelike infinity (i+) and study the smoothness of the solutions to the Einstein equations on the vicinity of i+.

Physical aspects of mots stability

Jaramillo J

The stability notion for marginally outer trapped surfaces (MOTS) plays a crucial role in the quasi- local study of black holes. Here we aim at offering some physical insight into this geometric concept by examining two particular examples. In the first one, we discuss the role of MOTS stability as the key element underlying a family of inequalities providing upper bounds for the black hole angular-momentum and charge in terms of the horizon area. In particular, these inequalities offer a characterization of black hole (sub)extremality in dynamical settings. In the second example we show that the spectral characterization of stability for stationary MOTS admits an interpretation as a Young-Laplace law for ”soap bubbles” in equilibrium. This second example further endorses the fluid analogies developed for black hole horizons in other contexts.

Radiation fields and vacuum solutions near time-like infinity

Friedrich H

We report on ongoing work with Piotr Chrusciel and Tim Paetz on the construction of vacuum space- times that admit smooth conformal extensions through past null infinity. The extensions are required to contain a point i, past time-like infinity, so that the boundary of the time like future of i represents past null infinity for the physical space-time. We wish to construct near the vertex of the future light cone N of the origin in Minkowski space, which is to represent past null infinity, smooth fields that satisfy at the vertex the conformal vacuum field equations up to a prescribed order and on the cone the constraints induced by the conformal field equations.

20 The radiation field, which represents the free datum on the cone N, is required to be smooth in a suitably sense. In certain coordinates, frame field, and conformal scaling which extends smoothly to a neighbourhood of the vertex it is then shown for all unknowns in the conformal field equations that their Taylor coefficients at the vertex can be calculated uniquely from the given radiation field. If there does exist a solution for the given data, tensor fields whose Taylor expansions at the vertex coincide with the ones derived here must satisfy the conformal field equations at all orders at the vertex. The present work concentrates on the algebraic problems which need to be solved to show that the constructions are indeed sufficient for the construction of solutions to the given null data.

On the characterization of non-degenerate foliations of pseudo-riemannian manifolds with conformally flat leaves

Gomez Lobo A

A necessary and sufficient condition for the leaves of a non-degenerate foliation of a pseudo-Riemannian manifold to be conformally flat is developed. The condition mimics the classical condition of the vanishing of the Weyl or Cotton tensor establishing the conformal flatness of a pseudo-Riemannian manifold in the sense that it is also formulated in terms of the vanishing of certain tensors. These tensors play the role of the Weyl or the Cotton tensors and they are defined in terms of the the curvature of a linear torsion-free connection (the bi-conformal connection). In addition we detail the geometric relevance of the bi-conformal connection in the invariant classification of conformally separable pseudo-Riemannian manifolds.

Black hole non modal linear stability

Dotti G

We prove that the space of linear perturbations off a stationary black hole can be parameterized using perturbed invariants of the Riemann tensor. This gives a norm to the space of solutions of the linearized equations, which allows to introduce the concept of pointwise boundedness of (generic) gravitational perturbations, as opposed to the standard bounds that apply only to pure harmonic modes.

Dynamic and thermodynamic stability of black holes and black branes

Wald R

I describe work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric pertur- bations: Dynamic stability is equivalent to the positivity of the canonical energy, E, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at in- finity and satisfy certain gauge conditions at the horizon. We further show that E is related to the second 2 P 2 2 order variations of mass, angular momentum, and horizon area by E = δ M − i Ωiδ Ji − (κ/8π)δ A, thereby establishing a close connection between dynamic stability and thermodynamic stability. Ther- modynamic instability of a family of black holes need not imply dynamic instability because the pertur- bations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to thermodynmi- cally unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of E is equivalent to the satisfaction of a “local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

21 Dynamic and thermodynamic stability of perfect fluid stars

Green S, Schiffrin J, Wald R

We explore the stability of stationary axisymmetric perfect fluid configurations to axisymmetric pertur- bations in general relativity. We consider the class of perturbations which keep the particle number, entropy, and angular momentum of each fluid element fixed. We show that the condition for dynamic stability with respect to such perturbations is equivalent to positivity of the canonical energy. Addi- tionally we show that, with respect to this class of perturbations, dynamic stability is equivalent to thermodynamic stability.

Gauge, energy and stability of black holes

Prabhu K , Wald R

Hollands and Wald showed that dynamic stability of a black hole is equivalent to the positivity of canonical energy on a space of linearised perturbations satisfying certain boundary conditions and gauge conditions. The boundary/gauge conditions are naturally formulated on the space of initial data for the perturbations in terms of orthogonality to gauge transformations. These perturbations can be uniquely specified in terms of transverse-traceless tensors. Using these transverse-traceless data, positivity of kinetic energy for perturbations can be proven. In certain special cases the potential energy can also be shown to be positive implying stability in these cases.

On the force between axisymmetric black holes

Gabach-Clement M

We present the problem of interacting black holes in axisymmetry and raise the question of existence of stationary multiple-black holes configurations. Making use of explicit solutions, Neugebauer and Hennig have recently shown that stationary two-components solutions do not exist. We look for an alternative approach to the problem of N¿=2 interacting, axisymmetric black holes and analyse the presence of a conical singularity on the bounded components of the symmetry axis. The deficit angle gives a measure of the force exerted by the holes onto each other. We obtain and discuss lower bounds on this force in terms of other physical parameters of the system (such as mass, angular momentum, electromagnetic charges and horizon area). We hope that further studies on this direction, in particular, focused on stationary solutions, might shed light on the problem.

Photon accumulation near a schwarzschild black hole

Perlick V , Philipp D

We discuss a gas of collisionless photons propagating on the Schwarzschild spacetime. We calculate the long-time behaviour of the photon distribution function for the case that photons are emitted isotropically from light sources distributed over a sphere of large radius R. In particular, we determine the resulting photon density between the horizon at r=2m and the light sphere at r=3m, both for static observers and for radially infalling (Painleve-Gullstrand) observers. We discuss if, for realistic stellar or supermassive black holes, this density can become so high in the course of time that it would be detrimental to the health of a hypothetical observer near r = 3m.

22 Future stability of models of the universe

Ringstroem H

The standard starting point in cosmology is the assumption that the universe is spatially homogeneous and isotropic. However, even if there is observational support for this assumption, it is clear that it is not exactly fulfilled. As a consequence, it is natural to ask: given initial data corresponding to a model of the universe, do small perturbations give rise to similar solutions? Motivated by this question, we shall discuss the question of future stability.

Existence and stability of dyons and dyonic black holes in einstein-yang-mills theory

Nolan B, Winstanley E

We study dyonic soliton and black hole solutions of the su(2) Einstein-Yang-Mills equations in asymptot- ically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we discuss the stability of these solutions under linear perturbations.. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.

Anti de sitter-like einstein-yang-mills spacetimes

Valiente Kroon J , L¨ubbe C

The purpose of this talk is to discuss the existence of solutions to the Einstein-Yang-Mills system for spacetime with an anti de Sitter-like Cosmological constant. To this end, the conformal Einstein field equations together with a gauge based on the properties of conformally privileged curves (conformal curves) is used to formulate a suitable initial-boundary value problem whose solution implies the existence of the required spacetimes. This analysis identifies a class of boundary data for the system consistent with the requirement of being maximally dissipative. To conclude, some remarks are made about the specific features of the spherically symmetric case — a system of current interest for numerical relativists. C. L´ubbe and J. A. Valiente Kroon. Anti de Sitter-like Einstein-Yang-Mills spacetimes. In preparation (2013). C. L¨ubbe and J. A. Valiente Kroon. On spherically symmetric anti de Sitter-like Einstein-Yang- Mills spacetimes. In preparation (2013).

23 Poster session

Highly relativistic spin-gravity coupling

Plyatsko R, Fenyk M, Stefanyshyn O

The Mathisson-Papapetrou (MP) equations are used for the description of spinning particle motions in Schwarzschild’s and Kerr’s background. It is of importance that the MP equations can be used for the investigation of spinning particle motions with any velocity relative to the source of the gravitational field, up to the speed of light, similarly as the geodesic equations are used for a fast moving spinless particle. We show that just at the highly relativistic spinning particle velocity its trajectory significantly differs from the corresponding geodesic trajectory due to the spin-gravity coupling. According to the MP equations in the comoving tetrad representation, a spinning particle ”feels” the gravitational field of the Schwarzschild mass that is proportional to the second power of the relativistic Lorentz factor as calculated by the particle velocity relative to this mass (this conclusion is common for the Mathisson- Pirani and the Tulczyjew-Dixon supplementary condition in the linear spin approximation). At high velocity the spin-gravity coupling causes the significant repulsive or attractive action, dependently on the correlations of the particle spin orientation and the direction of its orbital velocity, i. e. by the MP equations gravity has the clear features of strong antigravity. Probably, some effects of highly relativistic spin-gravity coupling can be revealed in astrophysical processes near compact sources of the gravitational field.

Localized periodic scalar field configurations in case of negative cosmological constant

Fodor G, Forgacs P, Grandclement P

On a fixed anti-de Sitter background both massive and massless real Klein Gordon fields can form exactly periodic spherically symmetric localized breather configurations. These solutions are known explicitly, and have a simple harmonic time dependence. Breather solutions also exist if the scalar field is self- interacting, but in that case they can be constructed only numerically, or by perturbative methods. In this talk I would like to present the structure of breathers when there is a fourth order interaction potential. The results are obtained by a spectral numerical code. A small-amplitude expansion procedure to study breather configurations will be also discussed. Similar localized periodic objects also exist for a self-gravitating scalar field when there is a negative cosmological constant. The presented scalar breather solutions can be considered as simple analogues of the non-spherically symmetric vacuum geon solutions which have been predicted to exist by perturbative methods in the asymptotically anti-de Sitter case.

Petrov classification on horizons of dirty black holes with axial symmetry

Tanatarov I , Zaslavskii O

We analyze the algebraic structure of the Weyl tensor in the vicinity of stationary dirty black holes with axial symmetry. The horizon can be of arbitrary extremality and distorted with matter, but is assumed to be regular. As observers staying outside of the black hole and the ones falling through the horizon are related by a singular Lorentz transform, with gamma factor diverging at the horizon, the algebraic structure in the two corresponding frames is in general different. The possible combinations of Petrov

24 types off-horizon and on-horizon, in the two frames of interest, are distinguished and classified. It is shown, in particular, that either off-horizon the space-time is of Petrov type D (or conformally flat) or the horizon is an algebraically special surface, on which the Petrov type is more special (and different in the two frames) than in its neighborhood. The alignment of principal null directions with respect to the generators and their asymptotic behavior are analyzed.

A survey of the anholonomic frame deformation method of constructing exact solutions

Vacaru S

We highlight the key ideas and methods of a geometric formalism for constructing generic off-diagonal solutions in general relativity and modifications. The new classes of solutions can be with Killing and non-Killing symmetries when the coefficients of metrics and connections depend, in general, on all space- time coordinates. It is sketched a proof that there is a general decoupling property of vacuum and nonvacuum Einstein equations written in variables adapted to certain classes of nonholonomic frames with 2+2 splitting. We show how such a geometric techniques can be applied for constructing generic off- diagonal exact solutions of the Einstein-Yang-Mills-Higgs (EYMH) equations. The corresponding classes of solutions are determined by generating and integration functions which may possess, or not, Killing symmetries. The initial data sets for the Cauchy problem and their global properties are analyzed. There are formulated the criteria of evolution of geometric/physical objects on spacetimes with nonholonomic splitting and decoupling of fundamental field equations. Examples of exact solutions defining (black) ellipsoid, toroid and solitonic configurations are provided.

Ultra-high energy collisions near black holes

Zaslavskii O

We suggest brief review of the effect of acceleration of particles by rotating and charged black holes to unbound energies in the centre of mass frame. Simple and general explanations of the effect are given: (i) the kinematic one based on the behaviour of relative velocity of colliding particles near the horizon, (ii) the geometric one, based on properties of particles’ four-velocities with respect to a local light cone near the horizon. The similar effect near the inner black hole horizon is also discussed and the role of the bifurcation point is revealed. We also discuss which energies can be detected by an observer at infinity.

Rainich-type conditions for null electrovacua

Torre C

Solutions of the Einstein-Maxwell equations with non-null electromagnetic fields have a purely geometric characterization via the classical Rainich conditions. Here I give analogous geometric conditions for solutions of the Einstein-Maxwell equations with null electromagnetic fields.

Understand law of precession during the merger of binary black holes

Wang C, Wu Y

We study a binary system of two non-rotating black holes with orbital angular momentum. During the merging process, when the apparent horizon first formed, the system becomes a single black hole with

25 the spin. From the theorem of black hole uniqueness, it will stabilize to a Kerr black hole at the final stage. In this work, we study the angular momentum radiations of the gravitational waves near the apparent horizon by using the non-linear full theory approach. The merger of the binary black holes is described by an algebraically spacial metric with the diverging and twisting null congruences, so the merging system contains two unknown functions (P (t, θ, φ) which is characterized by spatial area and L(θ, φ) which is characterized by angular momentum) for solving. We are able to extract the non-linear effects of gravitational radiations by analyzing the initial constraints of P and L, and the evolution equation of P . We aim to explain the law of precession during the binary black hole mergers from using similar Thorne’s asymptotically Cartesian and mass centered (ACMC-N) coordinate system of multipole expansion of gravitational radiation. It shows how to deduce the multipole momentums of a strong source from the form of such metric in an ACMC coordinate system. Further, to understand the spin-flip effects of this binary black hole system from spinning egg similarities and find the stability conditions from this construction.

Sen-witten equation does not have the node points in space of petrov type n

Pelykh V

The question about zeros of Sen-Witten equation (SWE) is a subject of investigations from the time of publication of Amitabha Sen work and introduction SWE by Edward Witten in proving of PET (1981), in connection with question about correlation between tensor and spinor methods in PET proving, and in connection with grounding of the tensor method, and also in connection with application of special orthonormal frame (SOF) in numerical relativity. Because SWE is elliptic of first order, the node points of its nontrivial solutions on manifold of dimension 3 do not create sets of dimension 2 or 3. For establishing conditions of node sets of lower dimensions absence we for the first time pointed [1], that the node points can be removed by choice of appropriate boundary condition and coefficients at spinor functions in squared SWE, and obtained such conditions. With application of these conditions we obtained also a conclusion about exact form of correlation between SWE and SOF [2]. As development and refinement of these results we present our new result. Theorem. Node points of SWE are absent in bounded closed region on space-like hypersurface in space-time of Petrov type N under fulfilling of the 1 2 1 πρ 1 2 1 πρ 1 2 1 πρ 2 following conditions: a) 2 K + 8 KπρK + µ ≥ 0, or 2 K + 8 KπρK + µ < 0, 2 (K + 8 KπρK + µ) − 1 2 2 2 16 [(∂1K) + (∂2K) + (∂3K) ] ≥ 0. b) in any point of the region boundary at most one component of Witten spinor do not vanish. Remarkably, that the hypersurface may not be maximal. 1. Pelykh V. Equivalence of the spinor and tensor methods in the positive energy problem. J . Math. Phys., 2000, 41, No. 8, P. 5550-5556. 2. Pelykh V. Comment on ”Self-dual teleparallel formulation of general relativity and the positive energy theorem”. Phys. Rev. D, 2005, 72, 108502.

Hamiltonian formulation of relativistic kinetic theory and applications

Zannias T , Sarbach O

We present a tangent bundle formulation of the relativistic kinetic theory of diluted gases propagating in an arbitrary gravitational field. Particular emphasis in this formulation is paid on the geometrical and symplectic structures, such as the Poincare one-form, the Liouville vector field as a Hamiltonian vector field, and the volume form on the mass shells. In our formulation, the Liouville or Vlasov equations emerge in a natural geometrical way. Some simple cosmological applications of these formalism are discussed.

26 Existence of a smooth family of null hypersurfaces surrounding a black hole in the presence of tails.

Moreschi O, Kozameh C, P´erezA

The dynamical description of the late phase of gravitational collapse (described by a black hole spacetime) remains an open problem in general relativity. A useful step in trying to solve Einstein’s equations in this very dynamical regime is to find a set of physically defined coordinates and associated frames that are well behaved both near the event horizon and at null infinity. Near null infinity the so-called Bondi coordinates provide a physical framework where the notion of momentum, angular momentum, and their flux laws adopt a very simple expression. Since the event horizon is approached in the limit where u (the retarded Bondi time) goes to infinity, the Bondi coordinate system can not describe the geometry in a neighborhood of the horizon. In this work we introduce afamily of null hypersurfaces w = w(u) which is regular at the event horizon, i.e., the function w should have a finite value as u → ∞. We show that the power-law decay modes found in linear perturbations of Schwarzschild black holes, generally called tails, do not produce caustics on a naturally defined family of null surfaces in the neighbourhood of i+ of a black hole horizon. This null congruence thus yields a well behaved coordinate system both near the event horizon and at null infinity.

The five dimensional story of dirac fermions and spherical black hole

NakoniecznyL

The interaction between matter and a black hole may be described in many ways. One of available tools to do this is field theory. Using this formalism we pursue a question of an influence of fermionic matter on a five dimensional static and spherically symmetric black hole. Some time ago it was revealed that the presence of massless electrically charged Dirac fermions in the spacetime of four dimensional dyonic Reissner-Nordstrom black hole leads to destruction of it. Considering this we check whether this is also true in case of five dimensional electrically charged black hole. We also explore the ways in which the mass of spinors influences this phenomenon. Another aspect of this problem is a question of existence of fermionic hair on five dimensional spherically symmetric black hole. In quest of finding the answers to this riddle we utilize spherical symmetry of the problem and use dimensional reduction to obtain an effective two dimensional system. Then we use bosonization technique to obtain a more compact description of the considered case. In the last step we use numerical methods to solve our equations.

General notion of total intrinsic angular momentum in general relativity

Gallo E, Moreschi O

The notion of total angular momentum at future null infinity has been the subject of numerous works. Different author have employed a variety of approaches that yielded nonequivalent definitions. In the case of a spacetime with axial symmetry due to the conservation property of Komar integrals, it is tempting to use as the appropriate notion of total angular momentum at future null infinity. But in a realistic situation the spacetime will not have any symmetries and the problem remains. Almost all of the suggested definitions, for the general case, suffer from the so called problem of supertranslations. However one of the authors was able to provide with a definition of intrinsic angular momentum which have circumvented those problems and also provided at the same time with the notion of center of mass at future null infinity. This approach was based on the notion of charge integrals of the Riemann tensor.

27 In this work we present the most general notion of intrinsic angular momentum, based on charge integrals approach, that is suitable for radiating spacetimes and do not suffer from supertranslations ambiguities. We also present the implications in requiring explicit agreement with the Komar integrals in the case of axial symmetry.

De donder-weyl hamiltonian formalism with constraints for general relativity

Kanatchikov I

We review the mathematical structures underlying the covariant De Donder-Weyl (DW) Hamiltonian formalism in field theory, such as the polysymplectic form, the Poisson-Gerstenhaber brackets on dif- ferential forms, and the representation of the field equations in terms of the brackets with the DW Hamiltonian function, which were found in our previous work. We also show how the Dirac bracket is generalized to this formalism for the singular field theories, in the sense of De Donder-Weyl, with the second class constraints. The example of the Einstein-Palatini action of vielbein gravity is elaborated in detail. We also discuss how the approach of the ”conversion of constraints” is generalized to the DW Hamiltonian formulation of vielbein gravity. The results of this classical analysis are being used in the so-called precanonical quantization of vielbein gravity (arXiv:1212.6963, arXiv:1302.2610) which requires neither the splitting into space and time nor infinite dimensional spaces of field configurations.

Gravitational equation in higher dimensions

Dadhich N

Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an al- ternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the Riemann curvature, and then the trace of its Bianchi derivative yields the corresponding polynomial analogue of the divergence free Einstein tensor defining the differential opera- (n) tor for the equation of motion. We propose that the general equation of motion is Gab = −Λgab + κnTab for d = 2n + 1, 2n + 2 dimensions with the single coupling constant κn, and n = 1 is the usual Einstein equation. It turns out that gravitational behavior is essentially similar in the critical dimensions for all n. All static vacuum solutions asymptotically go over to the Einstein limit, Schwarzschild-dS/AdS. The thermodynamical parameters bear the same relation to horizon radius, for example entropy always d−2n 2 goes as rh and so for the critical dimensions it always goes as rh, rh. In terms of the area, it would go as A1/n. The generalized analogues of the Nariai and Bertotti-Robinson solutions arising from the product of two constant curvature spaces, also bear the same relations between the curvatures k1 = k2 and k1 = −k2 respectively.

28 4d equations of motion and fifth force in a 5d general kaluza-klein space

Bejancu A

In this talk we present a new point of view on general Kaluza - Klein theories. A general KK space is a fibre bundle M over the 4D spacetime N , with 1-dimensional fibres. The semi-Riemannian metric g on M enables us to consider the orthogonal decomposition TM = HM + VM , where HM (resp.VM) is the horizontal (resp.vertical) distribution on M. Then we show that there exists a unique metric linear connection D on HM , whose torsion tensor field is just the extrinsic curvature of HM. Note that D plays in the general KK theory, the same role as the Levi-Civita connection on N in the classical KK theory.By using D and some horizontal tensor fields (including the 4D electromagnetic tensor field) we obtain , in a covariant form , the fully general 4D equations of motion in M . The main achievement of this new point of view on general KK theories , is that we give a new and correct definition of the fifth force along geodesics in M , and show that it does not contradict the 4D physics. In particular , we show that this force appears very rarely along geodesics in a warped 5D space , as it is for example , the Randall - Sundrum model. This is another reason which supports the idea that it is difficult to detect the fifth dimension.

Death and resurrection of the zeroth principle of thermodynamics

Rovelli C , Haggard H

The zeroth principle of thermodynamics in the form ”temperature is uniform at equilibrium” is notori- ously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the gen- eral context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the tem- perature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.

higher dimensional spinning einstein-yang-mills black holes

GHOSH S, PAPNOI U

We construct a Kerr-like spacetimes starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis, i.e., we extended Newman Janis algo- rithm in order to construct spinning BH from HD EYM BH. The new metrics are HD generalization Kerr-Newman spacetimes which has a geometry precisely that of Kerr-Newman in 4D, but the sign of charge term gets flipped in the HD spacetimes. It is interesting to note that gravitational contribution of Yang-Mills gauge charge is indeed opposite (attractive rather than repulsive) that of Maxwell charge. We also explore the two horizons: event horizons and static limit surface of spinning HD EYM BH, and also discuss the effects which comes from the YM gauge charged and also due to spacetime dimensions. We find that relative shape of the ergosphere grows with increasing spacetime dimension, and decrease with YM gauge charge.

29 Topology, rigid cosymmetries and linearization instability in higher gauge theories

Khavkine I

We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge transformations need not be in bijection. We also include the- ories with higher stage Noether identities, known as higher gauge theories (if they are variational). Some of these systems are known to exhibit linearization instabilities: there exist exact background solutions about which a linearized solution is extendable to a family of exact solutions only if some non-linear obstruction functionals vanish. We give a general, geometric classification of a class of these lineariza- tion obstructions, which includes as special cases all known ones for relativistic field theories (vacuum Einstein, Yang-Mills, classical N=1 supergravity, etc.). Our classification shows that obstructions arise due to the simultaneous presence of rigid cosymmetries (generalized Killing condition) and non-trivial de Rham cohomology classes (spacetime topology). The classification relies on a careful analysis of the cohomologies of the on-shell Noether complex (consistent deformations), adjoint Noether complex (rigid cosymmetries) and variational bicomplex (conserved currents). An intermediate result also gives a criterion for identifying non-linearities that do not lead to linearization instabilities.

The canonical superenergy tensors and stability of the solutions to the einstein equations

Garecki J

We have introduced in past the canonical superenergy tensors, for gravity and for matter, and studied of their applications in general relativity. Recently we have noticed that one can use these tensors to study of stability of the solutions to the Einstein equations. We formulate a suitable Proposition and give some examples.

On the zero set of solutions of the witten equation on asymptotically euclidean hyper-surfaces

Frauendiener J

It is well known that the Witten equation serves as a condition for a spinor field on an asymptotically Euclidean space-like hypersurface, which is used in Witten’s proof of the positivity of the ADM mass. Nester has suggested an alternative approach towards this result, which is based on the use of orthonormal frames on the hypersurface subject to some gauge conditions. Using the close relationship between a non-zero spinor on a hypersurface and an orthonormal frame one finds that the Witten equation and the frame gauge condition agree on maximal, asymptotically flat hypersurfaces. Now one may ask under which circumstances the Witten equation has non-vanishing solutions, corresponding to a globally defined orthonormal frame. In this talk we show that the property of having non-vanishing solutions is stable near the flat case and discuss some of the implications.

Jacobi fields in some static and cosmological spacetimes

Sokolowski L, Golda Z

Our investigation has been motivated by the twin paradox in curved spacetimes. Geometrically one can

30 only seek for a timelike curve joining two given points in the spacetime which has globally maximal length in the space of all timelike curves with these endpoints. This curve is a timelike geodesic with length equal to the Lorentzian distance function between the points. Unfortunately there is no local analytic tool (e.g. a differential equation) allowing one to seek for the maximal curve, what implies that there is no effective algorithmic procedure to find in a finite number of steps the geodesic which realizes the distance function. One can only find out the locally maximal timelike geodesics by investigating the Jacobi vector fields (solutions of the geodesic deviation equation) on a given geodesic. Our investigations show a multitude of possibilities concerning Jacobi fields and the conjugate points in a number of static spacetimes and Robertson-Walker cosmology. The Jacobi fields may be effectively studied only in spacetimes with a high symmetry since the existence of integrals of motion generated by Killing vector fields is crucial. In some cases of high symmetry (e.g. spherical one) it is possible to show that some locally maximal geodesics are actually the globally maximal ones.

Palatini formalism, levi-civita truncations, and lovelock gravities.

Pons J , Dadhich N

We review Einstein’s approach to the so called Palatini formalism of general relativity, using an arbitrary connection -thus possibly including torsion and non-metricity. We show that, contrary to the common lore, the original and the Palatini formulations (with an arbitrary connection!), are completely equivalent. We uncover a gauge symmetry that has been basically overlooked for a long time. When we try to extend the equivalence to higher order gravity theories, we uniquely obtain the family of Lovelock Lagrangians, out of the requirement of consistency of a Levi-Civita truncation.

3+1 and 2+2 decompositions and theirs geometries.

Wojnar A

Naveira’s classification of Lorentzian almost-product structures on spacetime manifolds is confronted with 3+1 and 2+2 decomposition of spacetime. The first splitting is related to the notion of a relativistic observer. It turns out that a choice of the observer (timelike normalized vector field) determines a geometry of spacelike distribution. Some examples of observers are shown. The 2+2 decomposition is connected with null congruences of curves (outgoing and ingoing light rays) and it is also possible to consider the geometry of spacetime due to optical scalars of light. The geometry of Schwarzschild interior solution is discussed.

Defining mass for black holes with scalar field hair in anti-de sitter spacetime

Toubal W

We investigate gravity minimally coupled to a scalar field in Anti-de Sitter (AdS) spacetime. We define and calculate the mass in matter-free AdS using an approach due to Henneaux. We obtain a set of boundary conditions which guarantee finite mass. We show that by introducing a scalar field with a self-interacting potential the asymptotic conditions are no longer satisfied. The scalar field has a slow fall off which modifies the geometry. An extra contribution to the mass from the scalar field subleading terms is needed to cancel divergences and obtain a finite mass. The mass is shown to depend on small terms in the expansion of the scalar field and the metric deviation. These terms are found numerically.

31 A reference for the gravitational energy

Chen C , Nester J, Liu J, Sun G

The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. The value of the Hamiltonian, corresponding to the quasi-local quantities, and the associated boundary conditions are determined by the boundary term. The boundary term requires a reference to determine the ground state with vanishing quasi-local quantities. For our preferred boundary term in general relativity we propose (i) 4D isometric matching, and (ii) extremizing the energy on 2 surface to determine the reference metric and connection values.

Isometric embeddings, general relativity and the cauchy problem

Willison S

We consider gravitational field equations in terms of free isometric embeddings, for which the second fundamental form is a collection of linearly independent vectors. The well known theory in 9+1 dimen- sions is cast in Cauchy-Kowalevski form and therefore local existence and uniqueness results follow for analytic initial data. In the case of smooth data, an existence theorem is lacking. We introduce a 13+1 dimensional theory, with an appropriate conserved initial value constraint fixing the isometric bending degrees of freedom. This allows us, in the neighbourhood of a free embedding, to obtain a system of hyperbolic differential equations. The theory is shown to be equivalent to GR (or massive Fierz-Pauli gravity) at the linearised level. We discuss the question of the global embedding of the initial value surface. The full non-linear theory and the question of global-in-time existence are formidable.

Identifying kerr geometry from covariant derivatives of the riemannian

Aman˚ J

It is shown how it is possible to determine if a certain line element is the Kerr (or Schwarzschild) black hole geometry from the Riemannian and its first two covariant derivatives. It is not straightforward to determine if an unknown metric is the same as a known metric, e.g. the Kerr metric, the equivalence problem. In particular, many other Petrov type D metrics have partly the same relations as the Kerr metric between the derivative components. A computer algebra program to basically automatic determine if an unknown metric is equivalent to the Kerr black hole metric, using the Newman-Penrose spinors and their first two covariant spinor derivatives, is presented. The Kerr parameters are determined.

Stable causality and higher dimensional black holes

Szybka S

I will present Hawking’s notion of stable causality and discuss it in the context of higher dimensional black holes.

32 Embedding hairy black holes in a magnetic universe

Astorino M

Ernst’s solution generating technique is extended to Einstein-Maxwell theory conformally (and mini- mally) coupled to a scalar field. This integrable system enjoys a SU(2,1) symmetry which enables one to move, by Kinnersley transformations, through the axisymmetric and stationary solution space, building an infinite tower of physically inequivalent solutions. As a specific application, metrics associated to scalar hairy black holes, such as the ones discovered by Bocharova, Bronnikov, Melnikov and Bekenstein, are embedded in the external magnetic field of the Melvin universe.

Analytic solutions of equations of motion with applications in astronomy

Laemmerzahl C , Hackmann E

The properties of space and time can be explored by the motion of particles. This includes the motion of pointlike test particles around black holes where general relativistic effects will show up like perihelion shift, Lense-Thirring effect, and light deflection. Based on that we also can discuss phenomena like the shadow of black holes and the light sphere surrounding black holes. More exotic effects are the motion on orbital cones, the travel into other universes, time travel, geodetic incompleteness, etc. Further important examples are the motion of test bodies with structure like spin and mass multipole moments which is much more complicated than the motion of point particles. Based on our recently found analytic solutions of general hyperelliptic differential equations we present the exact solutions of several equations of motion (for neutral pointlike test particles, for charged particles, and for particles with spin) in a large class of space-times and also analytically calculate the corresponding observables (perihelion shift, Lense-Thirring effect, gravitomagnetic clock effect, conicity, light deflection, and others). We also give examples which generalize the hyperellptic frame to quartic algebraic curves. These examples are the motion of test particles in Horava-Lifshitz and Gauss-Bonnet space-times or the motion of charged particles in regular black-hole space-times based on non-linear electrodynamics.

Conformally covariant systems of wave equations and their equivalence to einstein’s field equations

Paetz T

We transform Friedrich’s conformal field equations in 3+1-spacetime dimensions into two alternative systems of wave equations, supplemented by certain constraint equations, and study their equivalence (and thereby equivalence to Einstein’s vacuum field equations). As an application the characteristic initial value problem for the Einstein equations with data on past null infinity is reduced to a characteristic initial value problem for wave equations with data on a light-cone.

Trapped surfaces in the oppenheimer-snyder collapse

Bengtsson I, Jakobsson E, Senovilla J

Inside a dynamical black hole there is a region containing trapped surfaces as well as a region into which no trapped surface extends. But we do not know where the boundary between these two regions is.

33 We have constructed trapped surfaces passing through the center of the Oppenheimer-Snyder collapsing dust cloud, and argue that that they reach this boundary at the center. There is a marginally trapped round sphere where the surface of the collapsing star meets the event horizon, and this must be part of the boundary. We have proved that there is a spacelike separation between the location of the boundary at the center and at the surface of the star.

Extrinsic versus intrinsic angular measures along curved spacelike world lines

Ba˙za´nskiS

Let L be a spacelike curve such that the first of the Frenet formulae applied to its tangent vector e1 at the point p will render a spacelike normal vector e2 of L at p. When in a considered case one of the coordinates is an angle phi, then an arc A of L contained in the coordinate domain can be described by eqs. in terms of phi. Any numerical value of a geometric quantity (which was so far defined by an invariant integral along the arc A of an integrand being a function of phi and with phi as its integration variable) should, in my opinion, be considered as defined in the extrinsic angular measure. As the angle phi is induced at any point along L by an external coordinate, the value of the integral is measured in coordinate dependent radians. Recently I realised that in relativity there is another, physically well- grounded angular measure psi, purely geometrically determined along an arc A of L of a kind quoted above. It is intrinsically defined in the spacelike osculating plane at any point p of A, ie. defined by a set of Frenet tetrads eA(p) at any p along A. Because of this rather remote resemblance to the proper time, a suitable name of the unit of the intrinsic measure would be proper radian. These two concepts however differ from each other. It is eg. not possible to change in the usual way the integration variable from phi to psi, but one must instead replace the old integration limits by new ones expressed in terms of invariants, defined eg. by the Frenet tetrads.

34 A3 - Modified gravity theories

Oral session

Einstein-aether gravity: thermodynamics of universal horizons

Mohd A

The theories of gravity which violate local Lorentz invariance do not admit a universal maximum speed of signal-propagation. Different field excitation see a different effective metric and hence a different light cone. In these theories, although one can define the Killing horizon in a conventional way, this definition does not capture the notion of a black hole. This is so because there exist modes which see a wider light cone than the one defined by the Killing Horizon and therefore can escape to infinity. However, there exist solutions of these theories which admit a special spacelike hypersurface which is a one-way membrane. This hypersurface acts like a black-hole horizon and is called the Universal Horizon because it traps modes travelling with arbitrarily high velocities. In this talk, we show that we can use the Noether charge method ‘a la Wald to formulate a first-law, which resembles the first law of thermodynamics, for the universal horizons in Einstein-Aether theory. This seems to suggest that in Lorentz violating theories one should ascribe the thermodynamical properties to the universal horizon and not to the Killing horizon.

Bigravity and massive gravity in hamiltonian approach

Soloviev V , Tchichikina M

The Hamiltonian formalism of bigravity with ultralocal potential of general form, under some conditions put on the potential, has 4 first class constraints and their algebra in Dirac brackets is the well-known algebra of hypersurface deformations. If we suppose that the potential also satisfies a special degeneracy condition suggested by de Rham, Gabadadze, Tolley (dRGT), then the constraint algebra of bigravity is changed and we study this in detail. In contrast to other works on this subject we do not use neither the explicit form of dRGT potential nor the Hassan-Rosen transformation of variables, but follow some kind of axiomatic approach. Also we prefer Kuchar’s Hamiltonian formulation which involve embedding variables.

Weakly coupled massive gravity

Pilo L

We find a new class of theories of massive gravity with five propagating degrees of freedom where only rotations are preserved. Our results are based on a non-perturbative and background-independent

35 Hamiltonian analysis. In these theories the weak field approximation is well behaved and the static gravitational potential is typically screened ‘a la Yukawa at large distances, while at short distances no vDVZ discontinuity is found and there is no need to rely on nonlinear effects to pass the solar system 1/2 − tests. The effective field theory analysis shows that the ultraviolet cutoff is (m MP l) 10 3 m the highest possible. Thus, these theories can be studied in weak-field regime at all the phenomenologically interesting scales, and are candidates for a calculable large-distance modified gravity.

Ghost-free massive gravity in ashtekar variables

Speziale S

A generic self-interacting theory of a massive spin-2 particle is plagued by an instability known as the Boulware-Deser ghost. De Rham, Gabadadze and Tolley have recently proposed a special self-interaction for which the ghost is absent. Their special interaction has a cumbersome expression in the usual metric formalism, which leads to a difficult canonical analysis. In this talk I will show how massive gravity can be conveniently casted in Ashtekar variables, and the proof of ghost-freeness becomes much more clear and explicit. I’ll point out the relation to the Plebanski formulation of general relativity, and a difficulty concerning the interplay between reality conditions (needed in the case of Lorentzian signature) and parity-odd terms. Finally, I’ll briefly overview the nonetheless still present difficulties with massive gravity at the theoretical and phenomenological level.

The stability of de sitter solutions in bimetric gravity

Sakakihara Y

We construct de Sitter solutions in bimetric gravity and examine the stability of them. In bimetric gravity, there are two de Sitter solutions for the same parameters. However, by checking the Higuchi bound, we show that one of them is always stable and the other is not. Such difference occurs because the bifurcation point of two branches exactly coincides with the Higuchi bound. This result implies that the Higuchi bound selects the real de Sitter solution in bimetric gravity.

Vacuum structure of hoˇrava-lifshitz gravity

Melby-Thompson C

Because it has a freer structure than general relativity, Horava-Lifshitz (HL) gravity is able to exhibit interesting phenomena not present in Einstein gravity. This distinction is visible already at the level of its vacuum structure, which is characterized by a non-trivial phase diagram. Even in the case of negative cosmological constant, the vacuum structure is simple but interesting: in the asymptotic region the theory is characterized by ”Lifshitz space”, which is appropriate to holography for anisotropic field theories. We describe the novel structures arising from this freedom and discuss some of their implications and applications. In the process we cover some of the corresponding difficulties that arise, such as the definition of conformal infinity, black holes, and thermodynamic quantities; and the structural differences between the projectable and non-projectable versions of the theory.

36 Chronology protection conjecture and goedel models in horava-lifshitz gravity

Reboucas M

In the attempts toward a quantum gravity theory, general relativity faces a serious difficulty since it is non-renormalizable theory. Horava-Lifshitz gravity offers a framework to circumvent this difficulty, by sacrificing the local Lorentz invariance at ultra-high energy scales in exchange of power-counting renormalizability. The Lorentz symmetry is expected to be recovered at low and medium energy scales. If gravitation is to be described by a Horava-Lifshitz gravity theory there are a number of issues that ought to be reexamined in its context, including the question as to whether this gravity incorporates a chronology protection, or particularly if it allows Goedel-type solutions with violation of causality. We show that Horava-Lifshitz gravity only allows the chronology respecting regions of Goedel-type space- times, excluding therefore the noncausal regions of underlying Goedel-type manifolds. There emerges from our results that the famous noncausal Goedel model is not allowed in Horava-Lifshitz gravity. The question as to whether this quantum gravity theory permits Goedel-type solutions in the chronology pre- serving region is also examined. We show that Horava-Lifshitz gravity not only excludes the noncausal Goedel universe, but also rules out any hyperbolic Goedel-type solutions for physically well-motivated perfect-fluid matter content.

Stationary axisymmetric and slowly rotating spacetimes in hovava-lifshitz gravity

Wang A

Stationary, axisymmetric and slowly rotating vacuum spacetimes in the Hoˇrava-Lifshitz (HL) gravity are studied, and shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution found in general relativity.

Energy extraction and particle acceleration around rotating black hole in horava-lifshitz gravity

Abdujabbarov A, Ahmedov B, Ahmedov B

Penrose process on rotational energy extraction of the black hole (BH) in the original non-projectable Horava-Lifshitz gravity is studied. The strong dependence of the extracted energy from the special range of parameters of the Horava–Lifshitz gravity, such as parameter ΛW and specific angular momentum a has been found. Particle acceleration near the rotating BH in Horava–Lifshitz gravity has been studied. It is shown that the fundamental parameter of the Horava–Lifshitz gravity can impose limitation on the the energy of the accelerating particles preventing them from the infinite value .

37 Cosmology of generalized galileons

Kobayashi T

The generalized Galileon is the most general scalar-tensor theory having second-order equations of mo- tion. I will describe some cosmological applications of the generalized Galileon. I will show that the generalized Galileon is indeed equivalent to the most general scalar-tensor theory developed by Horndeski 40 years ago, and then explain in particular how the theory is used to study inflationary fluctuations, giving the most general action for cosmological perturbations. I will also comment on the multi-field generalization of the Galileon and its application to inflationary cosmology.

Nonlocal modifications of gravity

Woodard R, Deser S, Deffayet C, Esposito-Farese G

The only stable, local and metric-based modification of gravity if f(R) models. A much wider class of models arises if one considers nonlocal effective actions which might represent the of quantum corrections from the vast ensemble of gravitons produced during primordial inflation. I discuss models of this type, both to explain the current phase of cosmic acceleration and to avoid the need for dark matter. This talk is based on arXiv:0706.2151, 0904.0961 and 1106.4984.

Problems with nonlinearity of f(t) gravity

Ong Y , Izumi K, Nester J, Chen P

Teleparallel theories of gravity have long history, and include Teleparallel Equivalent of General Relativity [TEGR]. As an attempt to explain accelerated expansion of the universe, various models of modified gravity had been suggested in the literature, including the generalization of TEGR to f(T) gravity, which is analogous to extending general relativity to f(R) gravity. As with other modified theories of gravity, it is important to check the behavior of any extra degrees of freedom in f(T) Theory. We have found that these extra degrees of freedom are inherently very nonlinear, and is thus prone to cause various problems. We will discuss the cosmological perturbation of f(T) gravity to reveal the nonlinearity of the theory, followed by a discussion on superluminal propagating modes and ill-posed Cauchy problem in f(T) gravity. We will also give a brief comparison with massive gravity theory.

The finsler spacetime formalism: non-metric geometric backgrounds for physics

Pfeifer C

Finsler geometry in its standard formulation is an extension of Riemannian geometry derived from a general length measure for curves. For the application in physics it has the shortcoming that it is not capable to encode causality and the propagation of light in the null-structure of spacetime. During this talk I present the extension of the standard Finsler geometry formalism to our Finsler spacetime geometry framework. These Finsler spacetimes turn out to be a viable geometric background for physics: They admit a precise notion of causality and a coupling principle to matter field theories which determine the Finsler spacetime geometry dynamically through a gravitational field equation. The latter can be seen as

38 consistent extension of the Einstein equations, since in case the general Finsler spacetime geometry equals Lorentzian metric spacetime geometry the solutions of the more general dynamics are those from general relativity. I conclude with a first order perturbative solution of the dynamical equation, determining a non-metric Finsler spacetime which is a refinement of the linearized Schwarzschild solution of general relativity.

Methods of cosmological models selection

Godlowski W

One of the crucial problem of modern observational cosmology is the problem of discrimination between different cosmological models. This difficulty, called as the degeneracy problem is that many different scenarios are compatible with the present day observations. To solved this problem we use the combined analysis of astronomical data like supernovae type Ia (SNIa) data, Fanaroff-Riley type IIb (FRIIb), Radio Galaxy (RG) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) We use the Akaike and Bayesian information criteria of model selection to overcome this degeneracy and to determine a model with such a set of parameters which gives the most preferred fit to the data. Moreover we show that different cosmological models give different predictions for value of parameters like for example Ωm,0. These value could be compared with independent astrophysical measurements and as results they also could be used for discrimination between models.

Algebraically special exact solutions of quadratic curvature gravity theories

Malek T , Pravda V

We study exact vacuum solutions of quadratic gravity (QG) in arbitrary dimension. Besides the standard Einstein-Hilbert term, the Lagrangian of QG contains all possible polynomial curvature invariants up to the second order in the Riemann tensor. It turns out that all Weyl type N and a certain subclass of type III Einstein spacetimes with an appropriately chosen effective cosmological constant depending on the particular parameters of the theory are solutions of QG. Explicit examples of these solutions and of type III Einstein metrics not belonging to the mentioned subclass are presented. Then we investigate a wider class of spacetimes admitting a pure radiation term in the Ricci tensor. In contrast to the Einstein case, the source-free field equations of QG restrict the geometry and hence such solutions belong to the Kundt class. We also provide examples of these metrics.

Structure formation in a nonlocally modified gravity model

Park S, Dodelson S

We study a nonlocally modified gravity model proposed by Deser and Woodard which gives an expla- nation for current cosmic acceleration. By deriving and solving the equations governing the evolution of the structure in the Universe, we show that this model predicts a pattern of growth that differs from standard general relativity (+dark energy) at the 10-30% level. These differences will be easily probed by the next generation of galaxy surveys, so the model should be tested shortly.

39 Parameterized post-newtonian expansion and frw scalar perturbations in n-dbi gravity

Coelho F n-DBI gravity explicitly breaks Lorentz invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom. We look for observational consequences of this mode by computing the parametrized post- Newtonian (PPN) expansion of the metric to first post- Newtonian order. Surprisingly, we find that the PPN parameters are exactly the same as in General Relativity (GR), and no preferred-frame effects are produced. In particular this means that n-DBI gravity is consistent with all GR solar system experimental tests. We discuss the origin of such degeneracy between n-DBI gravity and GR and argue it holds in higher orders as well. We then proceed to study scalar perturbations of a generic Friedmann-Robertson- Walker space-time, wherein we show the scalar mode is always present and propagating, but decouples from the metric in the flat space limit. This results contradicts previous findings for perturbations around Minkowski space-time, where a static background was assumed a priori. We conclude that such assumption is too strong for theories invariant under foliation-preserving diffeomorphisms only, killing the very dynamics one is attempting to study and thus potentially leading to erroneous conclusions. Finally, we obtain explicit solutions for the scalar mode in the de Sitter vacuum of n-DBI and compare them with the behaviour of a minimally coupled canonical scalar field in a de Sitter space-time.

Solar system constraints on scalar tensor theories with non-standard action

Sen A

We compute the parametrized post-Newtonian (PPN), γ, for scalar tensor gravity theory when the action functional for the scalar field is a nonstandard one, namely, the Dirac-Born-Infeld type action, used in the literature for a tachyon field. We investigate two different cases (linear and conformal couplings) when the scalar field is non-minimally coupled to gravity via the scalar curvature. We find that the PPN parameter γ, which measures the amount of space curvature per unit rest mass, becomes a function of the effective mass of the scalar field. Using this PPN parameter, we calculate the time delay ∆τ for the signal to travel the round-trip distance between a ground-based antenna and a reflector placed in a spacecraft which is produced due to the gravitational field of the Sun. We use this ∆τ to compare our result with that obtained by the Cassini mission and derive the constraints on the model parameters.

Black holes in scalar-tensor gravity

Faraoni V

Hawking has proved that black holes which are stationary as the endpoint of gravitational collapse in Brans-Dicke theory (without a potential) are the same as in General Relativity. This result is extended to the much more general class of scalar-tensor and f(R) theories of gravity, without assuming any symmetries apart from stationarity. [Based on T.P. Sotiriou and V. Faraoni 2012, Phys. Rev. Lett. 108, 081103]

40 Detecting generic deviations from the kerr metric in black holes observed using gravitational waves

Moore C , Gair J

A space based gravitational wave detector, such as eLISA, would be expected to detect stellar mass compact objects inspiralling into the super massive black holes found at the centre of most galaxies. A detailed analysis of the signal from such an event offers an opportunity to test general relativity in the strong field regime. Approximate gravitational waveforms were calculated for such an event in a series of deformed Kerr metrics which retain the four constants of motion as familiar from the Kerr metric (in particular it retains a Carter-like constant). The Fisher matrix formalism was used to determine the accuracy to which the metric deformations could be measured for different leading order powers of (1/r) in the deformation. The results of the Fisher matrix analysis were then verified by using a Markov Chain Monte Carlo simulation to calculate the posteriors for a subset of parameters. Characterising the deformation to the metric with a dimensionless parameter of order unity, it was found that for a typical eLISA source the largest deformations (proportional to (1/r2)) could be constrained to a precision comparable to accuracy attainable on the other parameters with precision decreasing by approximately an order of magnitude for each power of (1/r).

Probing alternatives to general relativity with black hole observations

Some C , Gourgoulhon E, Grandclement P, Paumard T, Straub O, Vincent F

Observations with high angular resolution of the immediate vinicity of black holes are planned in the near future (GRAVITY/VLTI 2014, Event Horizon Telescope 2020). They offer a unique way to probe the metric around the central object and to compare with general relativity predictions (Kerr metric). We shall report on a systematic program of exploration of alternatives to the Kerr black hole and/or general relativity, showing results of numerical computations based on rotating boson stars, black holes in Einstein-Gauss-Bonnet theory, in Chern-Simons modified gravity or in Horava-Lifshitz gravity. In particular, we shall presents orbits of stars and images of accretion disks or tori around the black hole computed by combining numerical relativity codes (based on Kadath and Lorene library) and the new ray-tracing code Gyoto, focussing on the differences with respect to the Kerr case.

Fitting galaxies’ rotation curves without the need for dark matter or alternative theories of gravity

Magalhaes N , Cooperstock F

We illustrate how general relativity can be used to fit the rotation curves of galaxies without the need for dark matter or alternative theories of gravity. We model a galaxy as low density baryonic dust in stationary, axially-symmetric rotation, for which case it has already been shown that non-linear gravitational effects play a significant role in the overall motion of matter. The fits obtained were used to determine the mass densities as functions of galactocentric distances and heights, and yielded the galaxies’ masses. As a first approximation to their morphologies, we discovered that new information about the galaxies can be obtained from their mass-density functions. Our pproach is exemplified with the galaxies NGC 2403, UGC 128 and NGC 2903. We applied available astronomical information about them to illustrate how the approach can be used to investigate other galaxies. The surprisingly good results support and extend previous investigations and indicate that the preferred theory of gravity, general relativity, suffices to explain galactic rotation curves.

41 Detectability of scalar gravitational-wave bursts with ligo and virgo

Shawhan P, Sullivan S, Vedovato G, Coughlin S, Avara M, Drago M, Hayama K, Kamaretsos I, Klimenko S, Sutton P

Many alternative theories of gravity allow gravitational waves (GWs) to propagate with a scalar polar- ization mode (and possibly others) in addition to the two tensor modes predicted by general relativity. The scalar mode could even be dominant, particularly in the case of spherical collapse events of stellar cores or neutron stars. No explicit search for such signals has been carried out yet. In this work, we have studied the detectability of simulated scalar GW burst signals by the LIGO-Virgo network using slightly modified versions of standard GW burst search pipelines. We find that typical scalar burst signals can be detected well by these pipelines, which motivates carrying out actual searches in the future. Inter- estingly, scalar GW signals can be detected with nearly the same efficiency by an un-modified (tensor mode) all-sky burst search pipeline, although the source positions are misreconstructed.

Model-independent test of gravity with a network of ground-based gravitational-wave detectors

Hayama K , Nishizawa A

The observation of gravitational waves with a global network of interferometric detectors such as ad- vanced LIGO, advanced Virgo, and KAGRA will make it possible to probe into the nature of space-time structure. Besides Einstein’s general theory of relativity, there are several theories of gravitation that passed experimental tests so far. The gravitational-wave observation provides a new experimental test of alternative theories of gravity because a gravitational wave may have at most six independent modes of polarization, of which properties and number of modes are dependent on theories of gravity. This paper develops a method to reconstruct an arbitrary number of modes of polarization in time-series data of an advanced detector network. The method does not rely on any specific model, which gives model-independent test of alternative theories of gravity.

42 Poster session

Black strings-like objects as generators of a schwarzschild-de sitter braneworld

Da Rocha R

By performing a Taylor expansion along the extra dimension of a metric describing a black hole on a brane, we explore the influence of the embedding space on the black hole horizon. In particular, it is shown that the existence of a Schwarzschild-de Sitter correction of the black hole on the brane, in a braneworld scenario, might represent the radius of the black string collapsing to zero, for some point(s) on the black string axis of symmetry along the extra dimension. Based on a some developments on black string-like objects [1,2], we analyze the possibility of obtaining a region in the bulk, in a direction orthogonal to the brane, wherein the black string presents a radius equas zero. It is executed by investigating the black string associated to the mass shifted Schwarzschild brane black hole. Two distinct cases, where the bulk is considered as being dS5 or AdS5, are scrutinized. This presentation is further devoted to show the existence of a braneworld model providing a Kottler-like spherically symmetric brane metric. Delving into such black hole corrections by braneworld effects is elicited, the well-known results in the literature are recovered as limiting cases, and we assert and show that when the radius of the black string transversal section is zero, as one moves from the brane into the bulk, is indeed a singularity. [1] J. M. Hoff da Silva and R.da Rocha, Eur. Phys. J. C 72 (2012) 2258 [2] R. da Rocha, J. M. Hoff da Silva, Phys. Rev. D 85 (2012) 046009.

Modification of the newtonian dynamics in frw cosmology as alternative to dark matter and dark energy

Falcon N

Modified Newtonian Dynamics (MoND) is an empirically motivated modification of Newtonian gravity at largest scales, to explain rotation curves of galaxies, as an alternative to nonbaryonic dark matter. But MoND theories can hardly connect to the formalism of relativistic cosmology type Friedmann-Robertson- Walker. Presently work intends the existence of one scalar potential, with non gravitational origen, that would solve these problems. This potential Yukawa type inverse, is build starting from a reflection to speculate of the potential of Yukawa: null in very near solar system, slightly attractiveness in ranges of interstellar distances, very attractiveness in distance ranges comparable to galaxies cluster and repulsive to cosmic scales. The consequences of this potential are discussed, through Cosmological Model Tipe Friedmann-Roberston-Walker with cosmological term in function of the distance (lambda like fuction of r). In the cosmological model so raised the critical density of matter is consistent with the observed density does not include dark matter, MoND theory is deduted for interstellar scales and consequently would explain rotation curves. Also it is shown that Yukawa type inverse does not alter the predictions of the Cosmic Microwave Background neiher the primordial nucleosinthesys in early universe; and can be explain the large-scale structure formation.

43 Finite quantum gravity

Modesto L

We hereby present a class of higher derivative theories that realizes an ultraviolet completion of Einstein gravity. This class is marked by a non-polynomal entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high energy behaviour of the loop amplitudes. By power counting arguments, it is proved that the theory is (super-)renormalizable in any dimension, i.e. only one-loop divergences survive. Furthermore, in odd dimensions there are no counter terms for pure gravity and the theory turns out to be “finite”. Consequently, by introducing an infinite tower of massive states coming from dimensional reduction, quantum gravity is finite in even dimension, as well. Additionally, we propose a class of finite non-polynomial extensions of Horava gravity. These theories are ultra-local in the ultraviolet regime, unitary and stable for a negative value of the cosmological constant. At quantum level, the theories are ultraviolet finite because no logarithmic divergences occur. Some implications of this proposed class of theories are: asymptotic freedom, disappearance of singular- ities and decreasing of the spectral dimension at short distances. Some applications are: regular black holes, Starobinsky inflation and singularity-free Newtonian cosmology.

Eddington-inspired born-infeld gravity in three dimensions: solutions

Kar S, Jana S

Eddington-inspired Born–Infeld gravity in three spacetime dimensions is investigated. Analytical and numerical solutions for the scale factor in a three dimensional Friedman-Roberston-Walker (FRW) uni- verse with (i) pressureless dust and (ii) a perfect fluid with p=rho/2, as matter sources, are obtained. In addition, we also find a family of static, circularly symmetric analytical line elements with isotropic pressures. For the FRW cosmological models, we note that if the new parameter ‘kappa’ which arises in the theory, is positive (kappa¿0), the solutions are singular (except for the open universe, with a specific condition), whereas, if kappa¡0 they represent non-singular spacetimes. On the other hand, in the circularly symmetric static case, our solutions are found to be non-singular for both kappa¿0 and kappa¡0.

Off-diagonal deformations of kerr black holes in modified massive gravity and higher dimensions

Vacaru S

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in Ein- stein gravity and modified gravity theories when the field equations decouple with respect to certain classes of nonholonomic frames of reference. This allows us to construct various classes of exact solutions with Killing and non-Killing symmetries, when the coefficients of fundamental geometric/ physical ob- jects may depend on all spacetime coordinates. Our method can be extended to higher dimensions which simplifies some proofs for imbedded and nonholonomically constrained four dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. There are analyzed exact solutions de- termined by new type interactions and sources in massive gravity and/or modified f(R,T) gravity. We conclude that imposing nonholonomic constraints on generic off-diagonal nonlinear parametric interac- tions in general relativity we can mimic various locally anisotropic effects with alternative treatment in massive and/or modified gravity, and inversely.

44 Charged particles motion around rotating non-kerr black hole immersed in uniform magnetic field

Abdujabbarov A, Ahmedov B, Jurayeva N

Analytical solutions of Maxwell equations around rotating non-Kerr black hole immersed in external uniform magnetic field have been found. Then influence of magnetic field on effective potential of the radial motion of charged test particle around rotating non-Kerr black hole immersed in external magnetic field has been investigated by using the Hamilton-Jacobi equation of motion. The dependence of the minimal radius of the circular orbits rmc and radius of the innermost stable circular orbits (ISCO) from the deformation and the magnetic parameters for motion of charged particles around rotating non-Kerr black hole has been found. The increase of the magnetic field decreases the ISCO radius while the negative deformation parameter may lead to the bigger ISCO radius. Comparison of the numerical results on ISCO around non-Kerr black hole with the observational data for ISCO radius of rapidly rotating black holes provides the upper limit for the deformation parameter as leq22.

Loop quantum modified gravity and its cosmological application

Ma Y , Zhang X

A general nonperturvative loop quantization procedure for metric modified gravity is introduced. As an example, this procedure is applied to scalar-tensor theories of gravity, including f(R) theories. The quantum kinematical framework and dynamics of these theories are rigorously constructed. As an ap- plication to cosmological models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The classical differential equation which represents cosmological evolution is replaced by a quantum difference-differential equation. The effective Hamiltonian and modified dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology. The effective equations indicate that the classical big bang singularity is again replaced by a quantum bounce in loop quantum Brans-Dicke cosmology.

Connection dynamics of scalar-tensor theories of gravity in arbitrary dimensions

Han Y

As candidate modified gravity theories.Scalar-Tensor Theories have received increased attention in is- sues of dark Universe and nontrivial tests on gravity beyond GR,and modern theoretical physics re- search implies the existence of higher dimensional spacetime.The nonperturbative loop quantizasion of STT heavily relies on its connection dynamical formalism.Hence it is desirable to build the connection dynamics of STT in arbitrary spacetime dimensions.Our achievement in this paper is the detailed Hamil- tonian structure and connection dynamics in D+1 spacetime.By doing Hamiltonian analysis,we derive the Hamiltonian formulation of STT from the Lagrangian formulation.Two sectors are marked off by the D coupling parameter ω(φ).In the sector of ω(φ)eq − D−1 ,the canonical structure and constraint algebra D of STT are similar to those of GR coupled with a scalar field. In the sector of omega(φ) = − D−1 , the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained. The canonical structure and constraint algebra are also obtained. And next we succeeded to construct a Hamiltonian connection formulation of STT in arbitrary spacetime dimensions D+1 ≥ 3 using the gauge group SO(D+1) by canonical transformations from the geometry variables.We have also shown the constraint algebra is closed under the new connection variables.

45 From finsler spacetimes to observer space and vice versa

Hohmann M

We discuss two recent approaches to modify the Lorentzian geometry of spacetime in an observer- dependent fashion: Finsler spacetimes and Cartan geometry of observer space. The first is well-motivated as being the most general geometry that admits a geometric clock postulate, while the second has connections to ”canonical” approaches to gravity such as loop quantum gravity. We show that these frameworks, although rather different from a mathematical point of view, are in fact closely connected. Starting from a Finsler spacetime we present the construction of an observer space Cartan geometry. We show that also the converse construction is possible under certain conditions. These constructions are then applied to two different gravity theories: MacDowell-Mansouri gravity on observer space and Finsler gravity. We demonstrate how these theories can be translated from one framework to the other.

Structure of neutron stars in galileon modified gravity

GANGULY A, GANNOUJI R, JHINGAN S, MOTA D, RAY S, SANDSTAD M

We consider the covariant galileon gravity taking into account the third, fourth and fifth order scalar field Lagrangians with three, four and five derivatives acting on them respectively. We have also considered coupling between the Galileon field and the matter. The dynamical equations (the Kein-Gordon and the modified TOV) are set up for the system under consideration and is solved numerically for a Neutron star. Also we have performed perturbation analysis of the background derived previously. We studied the stability of the Regge-Wheeler and Zerilli equations. We have shown that the Vainshtein mechanism has given us results close to General Relativity for a large range of parameters for the model.

Hybrid metric-palatini gravities

Tamanini N , Bohmer C

The recently proposed hybrid metric-Palatini approach to modified gravity, where the action is taken to depend on a general function of both metric and Palatini curvature scalars, is revised. The dynamical equivalence with non-minimally coupled (bi)scalar field gravitational theories is explained. Applications to cosmology are presented showing presenting solutions and employing dynamical systems techniques.

Regge wheeler tensor for schwarzschild black holes in f(r) gravity

Goswami R, Nzioki A, Dunsby P

We develop a mathematical structure to study the covariant and gauge invariant perturbations of Schwarzschild black holes in f(R) gravity, using 1+1+2 covariant formalism. We unite the axial and polar degrees of freedoms into a single transverse traceless Regge Wheeler tensor, which is gauge invari- ant and frame invariant, and is a solution of the tensorial form of Regge Wheeler equation. We find the odd modes of perturbations to be exactly similar to General Relativity, while the presence of a scalar ”forcing term” in the wave equation for even modes makes these theories remarkably different for GR, that can be experimentally verified.

46 Orbits of brights stars as a tool to test gravity at the galactic center

Zakharov A, Borka D, Borka Jovanovic V, Jovanovic P

We found best fit parameters for Rn gravity and Yukawa gravity in case of orbits of S2-like stars. These theories of gravity have been proposed like alternative approaches to GR. These theories represents generalization of Einstein theory where the gravitational action (the Hilbert-Einstein action) is assumed to be linear in the Ricci curvature scalar R. In the case of f(R) gravity, one assumes a generic function f of the Ricci scalar R (in particular, analytic functions) and searches for a theory of gravity having suitable behavior at small and large scale lengths. One form of the extended theories of gravity are power-law fourth-order theories of gravity. Rn gravity like alternative approach to GR have been proposed. Rn gravity theory parameters have to be very close to GR ones from S2 star orbit. Another alternative approach to GR, Yukawa gravity, have been proposed. Yukawa-like corrections can been obtained in the framework of f(R) theories of gravity, the theory may be treated as version of f(R). We found best fit parameters of S2 star orbit in the framework of the Yukawa gravity. The best fit parameters for Yukawa gravity are non-vanishing and δ parameter is close to the value obtained for spiral galaxies recently.

Radiating kerr-newman black hole in f(r) gravity

GHOSH S, MAHARAJ S, PAPNOI U

We derive an exact radiating Kerr-Newman like black hole solutions to, constant curvature R = R0 imposed, metric f(R) gravity via complex transformations suggested by Newman-Janis. This generates a geometry which precisely that of radiating Kerr-Newman-de Sitter / anti-de Sitter with f(R) gravity term R0 contributing a cosmological-like term. The structure of three horizon-like surfaces, viz. timelike limit, apparent horizons and event horizons, are determined. We demonstrate the existence of additional cosmological horizons, in f(R) gravity model, apart from regular black hole horizons that exist in the analogous general relativity case. In particular, the known stationary Kerr-Newman black hole solutions, of f(R) gravity and general relativity, are also retrieved. It is seen that ergosphere is sensitive to the rotation parameter a as well as the parameter R0. It is interesting to note that timelike limit surface become more prolate thereby increasing area of ergosphere with increase in a, on the other hand the ergosphere region decreases with the the increase in the value of the parameter R0.

Eddington inspired born infeld gravity and coupling modification

Delsate T

We discuss a class of modification to the matter/gravity coupling coupling that does not introduce new degrees of freedom. We base the discussion on the specific example of Eddington inspired Born Infeld (EiBI) gravity. We briefly review the EiBI model and argue that all the interesting features such as singularity avoidance can be understood in terms of coupling modification. We also discuss pathologies of EiBI and possible extensions of the model. We finally propose a framework to change the coupling beetween matter and gravity without introducing new degrees of freedom, based on the specific case of EIbI. We discuss simlarities and differences with bimetric gravity models.

47 Reconstruction procedure in cosmological models with non-minimally coupled scalar fields

Vernov S

We employ the superpotential technique for the reconstruction of cosmological models with a non- minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained. The sufficient conditions to get a model with a polynomial potential have been analyzed.

Massive spin-2 fields on black hole spacetimes

Brito R

In this talk we develop the study of massive spin-2 fluctuations - including massive gravitons - around Schwarzschild and slowly-rotating Kerr black holes. This work has two important outcomes. First, we show that the Schwarzschild geometry is linearly unstable for small tensor masses, against a spherically symmetric mode. Second, we provide solid evidence that the Kerr geometry is also generically unstable, both against the spherical mode and against long-lived superradiant modes.

New nonlinear massive gravities and their cosmological applications.

Saridakis E

Very recently, a specific nonlinear extension of massive gravity was formulated, requiring the Boulware- Deser ghost to be systematically removed, which is free of the old vDVZ discontinuity problem, that is the zero-mass limit of the obtained results provides General Relativity results. Unfortunately, although consistent and promising, this new theory does not exhibit cosmological behavior in agreement with observations. We construct suitable extensions, such as varying mass massive gravity and partially massive gravity, which indeed lead to interesting cosmology, consistently with observations.

Precursor of inflation

Cho I

We investigate the evolution of the Universe driven by a scalar field with a quadratic potential in Eddington-inspired Born-Infeld gravity. The inflationary epoch appears naturally from the high-energy state of finite curvature for which quantum gravity is not necessary.

48 Palatini modified gravity cosmological models

Kamionka M

We argue that there is a huge amount of Palatini cosmological models faithfully reconstructing LCDM epoch. They may differ by initial and final scenarios. We have used the dynamical system methods in order to investigate dynamics of the models. Fitting free parameters we have demonstrated by statistical analysis that this class of models is in a very good agreement with the astronomical data.

Ppn parameters for scalar-tensor gravity with a potential

Jarv L, Randla E, Kuusk P, Hohmann M

We calculate the PPN ”parameters” alpha, gamma, and beta in the case of a static spherically symmetric source for scalar-tensor gravity with non-vanishing scalar potential in the Jordan frame. Since the ”parameters” depend on the radial coordinate we discuss the issue of defining them and compare with the computation of gamma in earlier papers.

Emergent lambdacdm model from brans-dicke theory

Hrycyna O, Szydlowski M

We study dynamics of the cosmological models with Robertson-Walker metric in Brans-Dicke theory using dynamical system methods. Due to Hartman-Grobman theorem we linearize dynamical system to obtain emergent evolution of current Universe in accelerating phase of its expansion. As a result we obtain the Hubble’s H2(z) function which generalizes evolutional equation in standard LambdaCDM model. We explain dark energy effect of acceleration and dark matter in terms of emergent dynamics rather than in terms of substantial form of dark matter and dark energy. Cosmological implications of obtained results are pointed out.

Data analysis for testing alternative theories of gravity with lisa pathfinder

Korsakova N , Hewitson M, Messenger C, Sathyaprakash B, Heinzel G, Danzmann K, Pannarale F

LISA Pathfinder (LPF) is a technology demonstration mission for LISA (Laser Interferometer Space Antenna), the principal elements of which are the two free floating test masses and the high precision optical metrology system that will measure the distance between the test masses to the picometer preci- sion. This gives us the opportunity to measure the gravity stress tensor with the corresponding precision. Taking into account the frequency band and the characteristic velocities of the free falling bodies in the Solar System the instrument may be sensitive to any anomalous deviations from the Newtonian Gravity in the vicinity of the saddle points of the gravitating bodies, for example, the Sun Earth saddle point. This talk will introduce a possible mission extension to fly to the saddle point to test alternative theories of gravity. Here the data analysis associated with such mission will be described in detail. In particular the parameter estimation for the various theoretical models and the conclusions that it would be possible to make based on the result of the experiment.

49 Dilaton gravity in brane scenarios and the large-scale structure challenge

Konikowska D

In this work we establish the effective 4-dimensional description of a theory of dilaton gravity in a 5- dimensional brane scenario, with dilaton non-minimally coupled to the matter content of the universe localized on the brane. Treating the matter as an inhomogeneous perfect fluid, we derive an upper bound on the spatial derivative of its energy density. Combining it with null results in the Newton’s constant time variation searches, we show that the cosmological large-scale structure as is observed today cannot exist on the brane for a commonly assumed exact anti de Sitter type bulk. Consequently, we investigate the possible generalizations of this simple string theory motivated scenario.

Energy conditions in modified gravity

Reboucas M

In standard approach to cosmological modeling in the framework of general relativity, the energy con- ditions play an important role in the understanding of several properties of the Universe, including singularity theorems, the current accelerating expansion phase, and the possible existence of the so- called phantom fields. Recently, modifications of Einstein’s gravitation theory have been used as an alternative to dark energy for the description of the accelerated expansion. If gravity is described by a modified gravity there are a number of issues that ought to be reexamined in the framework of these modified theories, including the classical energy condition. We discuss the formulation of the energy conditions in the framework of modified gravity. The null and strong energy conditions in the framework of a modified gravity theory are derived from the purely geometric Raychaudhuri equation along with the requirement that gravity is attractive. The weak and dominant energy conditions are then obtained in a direct approach via an effective energy-momentum tensor. We show that the energy conditions in modified gravity formally differ from energy conditions of general relativity, but reduce to well-known energy conditions in the suitable limit when the modified gravity reduces to GR.

Power-law behaviour of gravitational lensing in f(r) theories of gravity

Hobill D, Hovarth Z, Gergely L, Capozziello S, De Laurentis M

Gravitational lensing has become a useful tool for exploring spacetime structure. It can also be used to distinguish between different theories of gravity. Using a general solution obtained f(R) = Rn gravity theories that describes a compact object, the bending angle for gravitational lensing has been com- puted in the weak lensing approximation. The appropriate lens equation constructed from geometrical considerations can then be used to compute the angular positions and the brightnesses of the lensed images. Absolute measurements can be avoided by making observations of the image separations and the ratio of the brightnesses. It is found that for large image separations where distinct images can be resolved, the ratio of the brightnesses µ1/µ2 as a function of the image separation (θ1 − θ2) exhibits power-law behaviour where the exponent depends upon the power of the Ricci scalar appearing in the gravitational Lagrangian. This provides a means to observationally distinguish between different gravitational theories. Similar behaviour has also been shown to exist in higher dimensional gravity theories.

50 A4 - Complex and conformal methods in classical and quantum gravity

Oral session

Cosmological twistors

Penrose R

CosmolWith positive Λ, null infinity is spacelike and asymptotic twistors are associated with complex null geodesics at infinity. Comformal cyclic cosmology implies that this applies also to a twistor theory of the Big Bang. The relation between the two is mediated time-asymmetrically by the contact geometry of real null geodesics.

Newton’s 2nd law, radiation reaction & type ii einstein-maxwell fields

Newman E

We study first-order perturbations off the Reissner-Nordstrom metric, the perturbations remaining in the class of type II Einstein-Maxwell metrics. After all radial integrations (already in the literature) have been performed there remains four relevant field equations for 4 variables (a Weyl and 2 Maxwell tensor components & a direction field), with a reality condition. These variables and equations are expanded in spherical harmonics up to the quadrupole term. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstrom particle) the Bondi momentum of the particle takes the form of massxvelocity plus an electromagnetic radiation reaction term. The Bondi mass loss equation becomes the classical gravitational and electromagnetic (electric & magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation becomes Newton’s 2nd law with the Abraham-Lorentz-Dirac radiation reaction force and a momentum recoil (rocket) force. The reality condition on the Bondi mass aspect yields the conservation of angular momentum. It must be emphasized that these results do not involve any model building or any mass renormalization. They are results simply sitting peacefully in the type II equations waiting to be seen. There was no integrations past the radial ones. The velocity is associated with the existence of the shear-free null geodesic congruence arising from the type II condition.

51 On the conformal structure of the extremal reissner-nordstr¨omspacetime

Valiente Kroon J , L¨ubbe C

The purpose of this talk is to present a discussion of the properties of the extremal Reissner-Nordstr¨om spacetime in a neighbourhood of timelike infinity i+. To this end the conformal Einstein field equations together with a gauge based on the properties of conformal geodesics is used to show that i+ admits a representation in which the evolution equations and the various conformal fields are regular. This analysis is expected to be of relevance in the analysis of the stability (or not) of the extremal Reissner-Nordstr¨om spacetime. C. L¨ubbe and J. A. Valiente Kroon. A class of conformal curves in the Reissner-Nordstr¨omspacetime. Available at arXiv:1301.5458[gr-qc] C. L¨ubbe and J. A. Valiente Kroon. Conformal properties of the extremal Reissner-Nordstr¨omspacetime. In preparation.

The einstein field equations for the conformal scalar field in higher dimensions

Luebbe C

The energy momentum tensor for a conformal scalar field in n¿3 dimensions is derived using the con- formally invariant tractor formalism. Moreover the tractor formalism is used to derive the conformal Einstein field equations for a conformal scalar field in dimensions n¿3. The results presented here include a cosmological constant and the case of the non-linear conformal wave equation.

Supersymmetry and einstein weyl structures

Gutowski J

Three-dimensional Einstein-Weyl geometries are obtained from anti-self-dual 4-dimensional manifolds, or complexified hyper-Kahler manifolds, which admit a conformal symmetry. Significant progress has been made in classifying supergravity solutions in various dimensions, and Einstein-Weyl structures are found in these classifications. I will describe how such geometries arise naturally in a number of settings, such as conditions on solutions in Euclidean four-dimensional supergravity, and as conditions on the spatial cross sections of black hole event horizons in five dimensional supergravity.

Einstein-weyl geometry and webs

Krynski W

We construct Einstein-Weyl geometry out of Veronese webs which were introduced by Gelfand and Zakharevich as reductions of bi-Hamiltonian structures of certain type. We exploit the correspondence to show that Einstein-Weyl structures of the hyper-CR type are locally given in terms of solutions to the dispersionless Hirota equation. We also discuss connections between Einstein-Weyl geometry and third order ODEs.

52 Twistors and almost k¨ahlermodels of einstein and finsler spaces

Vacaru S

We provide an introduction into the geometry of spinors and twistors for (generalized) Finsler spaces and apply such geometric methods for constructing generic off–diagonal exact solutions of the Einstein and Ricci soliton equations. The key idea is to use the Cartan-Finsler connection on tangent bundles and on (semi) Riemannian / Lorentz manifolds enabled with nonholonomic (non-integrable) distributions. Such spaces are modelled equivalently as almost K¨ahlergeometries with nonholonomically induced torsion completely defined by the metric and related almost symplectic structures. In a particular case, we can consider fibred structures with 2+2 nonholonomic frame decompositions on Einstein manifolds and work alternatively (to the Levi-Civita connection) with Cartan-Finsler like connections. In such variables, the nonholonomic Einstein and twistor equations decouple and became integrable in very general forms, with respect to adapted frames. This allows us to generate various classes of non (anti) self-dual exact solutions and define global (Finsler like) twistors. At the end, it is possible to impose additional constraints resulting in zero torsion and Levi–Civita configurations. We provide a number of examples of exact solutions with solitonic, warped/traped configurations, (non) commutative branes and strings, black ellipsoid and anisotropic cosmological solutions and analyze their twistor classical and quantum models.

Complex and spinorial approaches to higher-dimensional general relativity

Taghavi-Chabert A

The aim of this talk is to present the recent progress made in the study of totally null (complex) m-plane distributions on 2m-dimensional real or complex pseudo-Riemannian manifolds. In the Lorentzian case, these give rise to the notion of Robinson manifolds, which are one generalisation of shearfree congruence of null geodesics from four to higher dimensions. As such, they have played a crucial role in the discovery of algebraically special solutions of Einstein’s equations. From Cartan’s work, a null plane distribution can be thought of as a projective pure spinor field. We introduce a higher-dimensional notion of principal pure spinors for the Weyl tensor, which in a sense, leads to a new higher-dimensional Petrov-Penrose classification of the Weyl tensor for complex and real split- signature manifolds. We also give a classification of the intrinsic torsion associated to such distributions - this is a split signature analogue of the Gray-Hervella classification of almost Hermitian manifolds. In this context, we discuss how the Goldberg-Sachs theorem, which relate the algebraic properties of the Weyl tensor to the integrability of a null plane distribution, can be extended to higher dimensions. As an application, we describe the curvature of the conformal extension of a projective structure.

Cr structures allow a new second-order ode to determine some twisting type n einstein spaces

Finley J

The 3-parameter foliation associated with a twisting principal null direction of an Einstein space can be modeled by a 3-dimensional CR manifold, which then provides a different basis for the study of such spaces. We have reduced the type N problem to one real and one complex pde; however, requiring also a Killing vector, invariance under the symmetry group of the pde’s, andΛ not 0 reduces this to finding the solution of a single, second-order ode for g(w), namely 2gg”+(g’+2w)2+(20/3)g+4C =0; with C either 1 or 0. A particular family of solutions may be described as infinite series about w = 0, well approximated by parabolas, with singularities only off the real w-axis. The series terminates only for the

53 Leroy-Nurowski solution, and for the one member which is conformally flat. The Cartan characters are used to distinguish inequivalent solutions. For Λ ¿ 0 they can be interpreted as transverse gravitational waves propagating in the de-Sitter background, with amplitudes proportional to Λ, generalizing the known non-twisting case. The method can also be extended to types III and II, with then a pair of ode’s that can give new solutions, with all values of Λ allowed.

Non-commutative twistor space and curved space-time

Penrose R

A novel approach to twistor theory in conformally curved space-time is suggested, where twistor spaces are patched together via non-commutative holomorphic geometries. Although motivated by the need for a twistor theory of conformally curved classical space-time, this specific approach is driven by quantum considerations.

From quantized twistors to noncommutativity of space-time

Lukierski J

We consider composite space-time coordinates expressed by primary two-twistor space components. The standard U(2,2)-covariant quantization procedure leads to the algebra of noncommutative space-time, with the noncommutativity given by the relativistic spin tensor, defined as nonorbital part of Lorentz algebra generators. Such a spin tensor generates infinite-dimensional spin algebra, which for particu- lar realizations becomes closed finite-dimensional algebra. One can conclude that quantum-mechanical twistoor coordinates generate noncommutative space-time structure, which is often considered as basic paradygmatic feature of quantum gravity framework.

Loop quantum gravity, twisted geometries and twistors

Speziale S

Loop quantum gravity is a background-independent approach to the quantization of general relativity. While the theory is continuous at the fundamental level, it is often useful to consider a truncation thereof, defined on the lattice dual to a graph. This truncation captures a finite number of degrees of freedom, which have been shown to describe a certain generalization of Regge geometries, called twisted geometries. In this talk, I will give a brief overview of the theory and its geometric interpretation. Then, I will describe how these discrete geometries can be described in terms of a collection of twistors associated to the lattice, thus providing a new sense in which twistors can be seen as non-linear gravitons. Finally, I will briefly discuss how dynamical transition amplitudes can be represented as integrals in twistor space.

Spin and center of mass in asymptotically flat spacetimes

Kozameh C , Quiroga G

We define the center of mass and spin of an isolated system in General Relativity. The resulting relation- ships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their newtonian counterparts, though no postnewtonian approximation has been

54 taken. We also derive equations of motion linking their time evolution to the emitted gravitational radi- ation. These equations should be useful when describing highly energetic processes where a considerable fraction of the total mass is emitted as gravitational waves.

Gravity in twistor space

Mason L

Recently there have been some remarkable new formulations of gravity in twistor space. In particular the entire tree-level S-matrix for (super)gravity can be expressed on twistor space in a particularly compact form. In this talk we review the geometry of the constructions, their proof following arXiv:1207.4712 and their relations with twistor actions and twistor-string theory if there is time.

Quantum twistor theory and the big bang

Sparling G

I will discuss the basics of quantum twistor theory, with particular attention to the question of the breaking of conformal invariance. I will place this theory in the context of a possible scenario for the development of the big bang.

Partner symmetries, group foliation and lift of non-invariant solutions of heavenly equations from 3 to 4 dimensions.

Sheftel M , Malykh A

We construct group foliation for the full system of six equations including elliptic complex Monge-Ampere equation and equations for its partner symmetries. For this purpose we obtain the full set of differential invariants up to 2nd order inclusive and operators of invariant differentiation. We derive resolving and automorphic equations and consider the problem of solving the resolving equations to obtain a lift from non-invariant solutions of Boyer-Finley equation to those of complex Monge-Ampere equation. Such solutions will generate anti-self-dual Ricci-flat (vacuum) metrics without Killing vectors. Thus they will posses one feature characteristic of K3 gravitational instanton.

Null killing and null homothetic killing vectors and their connection with geometry of null strings.

Chudecki A

Einstein complex spacetimes admitting null Killing or null homothetic Killing vectors are studied. These vectors define totally null and geodesic 2-surfaces, the null strings (twistor surfaces). As it follows from Sachs - Goldberg theorem both self-dual and anti-self-dual parts of the Weyl tensor of such spaces are algebraically degenerate. Consequently, the spaces considered are hyperheavenly spaces (HH-spaces) or, if one of the parts of the Weyl tensor vanishes, heavenly spaces (H-spaces).

55 All complex spacetimes admitting null homothetic Killing vector are found. It is shown, that all such spaces are hyperheavenly spaces with Lambda=0 of the types [III]x[N] or heavenly spaces with Lambda=0 of the types [III,N]x[-]. Complex spacetimes with null Killing vector and Lambda=0 can be only of the types [II]x[II], [D]x[D] or [III,N]x[N]. We present metrics of the above types. Null isometries with Lambda e 0 are also presented. Geometric properties of the null strings generated by the null Killing vectors are also discussed.

56 Poster session

The existence of time, part ii: time in general relativity from conformal symmetry

Hazboun J , Wheeler J

We show that the Lorentz structure of spacetime and the Einstein equation may be derived as part of the solution within a conformal gauge theory of Euclidean space. Quotients of the conformal group of n-dim (pseudo-)Euclidean spaces by their Weyl subgroups are called biconformal spaces. These naturally include both metric and symplectic form. We start from two known results. First, these spaces allow a scale-invariant action linear in the curvatures, making this theory distinct from the quadratic-curvature, Weyl gravity theory. The linear action leads to general relativity on the configuration submanifold. Second, flat solutions in the Euclidean case that are metric phase spaces are necessarily Lorentzian; time arises as part of the solution in a Euclidean theory. We generalize, combining these results. We show that Lorentz symmetry and the Einstein equation follow from the Euclidean gauge theory with linear action when the biconformal space admits orthogonal metric configuration and momentum submanifolds, assuming only separability of the torsion field equation. The separable field equations lead generically to a signature (n-1,1) metric, with orthogonality of the conjugate submanifolds leading directly to the compatible Lorentzian connection on both. We find exact solutions in which the Weyl vector is hypersurface orthogonal to spatial slices of the configuration and momentum submanifolds. We discuss relationships to shape dynamics and models breaking Lorentz invariance.

The existence of time, part i: phase space as conformal geometry

Wheeler J , Spencer J

Relativistic phase spaces built as gauge theories based on the quotient of the conformal group of n- dim (pseudo-)Euclidean spaces by their Weyl subgroups are called biconformal spaces. These naturally include both metric and symplectic form - structures usually imposed by fiat on phase spaces. These spaces are also known to allow a scale-invariant action linear in the curvatures in any dimension, with torsion-free solutions requiring Ricci-flat configuration spaces, making these conformal theories distinct from the quadratic-curvature, Weyl gravity theory. In these solutions, the full space is the co-tangent bundle of the configuration space. The Killing metric induces a metric on the configuration space, but is degenerate on the co-tangent spaces. We show that it is possible to find co-tangent bundles with non-degenerate metrics on both configuration and momentum subspaces, but these have signature different from that of the n-dim space which was initially gauged. In the zero curvature case, we induce Lorentzian metrics on the submanifolds from the Killing metric by gauging a Euclidean space. Using the natural metric and symplectic form, there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In Euclidean cases, the resultant configuration space must be Lorentzian and must remain so if curvatures are added perturbatively. In this context, time may be viewed as a derived property of gravity.

57 Palatini-weyl gravity as a conformal gauge theory

Wheeler J , Trujillo J

We revisit the Weyl-curvature-quadratic action of conformal gravity within the context of a conformal gauge theory, extending the action by the inclusion a dilatational curvature squared term. When treated in this way, it is natural to vary all gauge fields (a la Palatini), rather than only the metric. We show that all solutions of the resulting, more restrictive, field equations lie in conformal equivalence classes of Ricci-flat spactimes. Thus, vacuum solutions in Palatini-Weyl gravity are a subset of vacuum solutions to general relativity. We also find that while the theory has three candidates for gravitational energy contributions, quadratic in the Weyl curvature, Eisenhart tensor, and dilatational curvature, respectively, the first vanishes identically while the other two vanish as a consequence of the field equations.

A spin weight zero formulation of general relativity

Rojas T, Bordcoch M , Kozameh C

We present a set of three PDEs for three real scalars that are equivalent to the full Einstein equations without any symmetry assumptions. The main variables in this formulation, originally given in the Null Surface Formulation of General Relativity (NSF), are null surfaces and a conformal factor. Furthermore, for asymptotically flat spacetimes the free data representing gravitational radiation enters as the source term in the resulting equations. As a preliminary step we present peeling in NSF, i.e., the behavior of our variables as one approaches null infinity and show how the free data enters as the source term in the equations. We also show that the field equations adopt an extremely simple form if we assume that the spacetime points are close to null infinity. As a bonus we also give the equation governing the intersection of null cones from points with null infinity. This is specially important for the definition of the woeldline of the center of mass in general relativity.

58 B1 - Relativistic astrophysics

Oral session

Nuclear physics experiments with gravitational wave interferometers

Melatos A

Neutron stars are currently the only natural settings where one can study experimentally the funda- mental physics of bulk nuclear matter in the low-energy (MeV), many-body (1050 nucleon) regime. Gravitational waves (GWs) in the hectohertz band provide unprecedented opportunities to explore this physics by observing directly the internal motions of neutron stars. With the imminent commissioning of Advanced LIGO, such studies are poised to deliver significant new results; even today, GW upper limits on nuclear quantities are challenging terrestrial heavy-ion collider experiments. Here we review, by way of concrete multi-messenger examples, how GW and electromagnetic data can be jointly inverted to infer the thermodynamic coefficients (e.g. compressibility, viscosity), state of superfluidity, and electrical properties (e.g. resistivity, magnetization) of nuclear matter. Specific sources and the associated data analysis strategies will be reviewed, including rotational glitches from neutron stars (governed by the physics of quantized vortices) and surface mountains of thermal and/or magnetic origin (governed by the impurity abundance and processes like neutron capture in the stellar crust).

How high a hill can a neutron star have?

Owen B, Johnson-McDaniel N

Quadrupolar hills on a spinning neutron star emit gravitational waves, and thus the highest hill possible tells us the loudest gravitational-wave signal we can hope for. Previous calculations of the maximum quadrupole sustainable by elastic forces have neglected general relativity, despite the significant contri- bution from the self-gravity of the perturbation. We describe a general relativistic method for calculating these maximum quadrupoles, show that relativistic effects can reduce the maximum quadrupole by nearly an order of magnitude, and present maximum quadrupoles for a variety of neutron stars, quark stars, and hybrid stars.

Dark matter distributions around massive black holes: a general relativistic analysis

Will C , Ferrer F, Sadeghian L

The cold dark matter at the center of a galaxy will be redistributed by the presence of a massive black hole. The redistribution may be determined by beginning with a model distribution function for the

59 dark matter, and “growing” the black hole adiabatically, holding the adiabatic invariants of the motion constant within the distribution function. Unlike previous approaches, which adopted Newtonian theory together with ad hoc correction factors to mimic general relativistic effects, we carry out the calculation fully relativistically, using the exact geometry of the black hole. We consider a range of initial distribution functions, including “cuspy” profiles, and find that the density spike very close to the black hole is significantly higher than that found previously by quasi-Newtonian analyses. We will discuss potential implications for detection of signals from galactic center dark matter, and the effects of such a mass distribution on the orbits of stars very near the black hole.

Universal i-love-q relations in neutron stars

Yagi K , Yunes N

We find universal relations between the moment of inertia I, the Love numbers and the quadrupole moment Q that are essentially insensitive to the neutron star’s internal structure. These I-Love-Q relations lead to three immediate applications. On the observational astrophysics front, a measurement of any single member of this trio automatically determines the other two, thus providing information about quantities that may not be observationally accessible. On the gravitational wave front, the Q- Love relation breaks the degeneracy between spins and the quadrupole moment in inspiraling binary neutron stars waveforms, thus allowing for a direct measurement of the averaged spin given a detection with a second-generation ground-based detector, such as Adv. LIGO. On the fundamental physics front, the independent measurement of any two quantities in the I-Love-Q set, for example by combining millisecond binary pulsar observations with future gravitational wave detections, immediately allows for a model-independent and equation-of-state independent tests of General Relativity, and in particular, of one of its pillars, the strong-equivalence principle, that are orders of magnitude stronger than current Solar System ones.

Pulsar glitches: the crust is not enough

Andersson N

Pulsar glitches are traditionally viewed as a manifestation of vortex dynamics associated with a neutron superfluid reservoir confined to the inner crust of the star. In this talk I will demonstrate that the nondissipative entrainment coupling between the neutron superfluid and the nuclear lattice leads to a less mobile crust superfluid, effectively reducing the moment of inertia associated with the angular momentum reservoir. Combining the latest observational data for prolific glitching pulsars with theoretical results for the crust entrainment, we find that the required superfluid reservoir exceeds that available in the crust. This challenges our understanding of the glitch phenomenon, and I will discuss possible resolutions to the problem.

General relativitivistic plasma magnetospheres of slowly rotating and oscillating magnetized neutron stars

Morozova V, Ahmedov B, Zanotti O

The magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime is studied. We analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the

60 accelerating electric field and on the charge density. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with m = 0, 1 are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode (l,m) = (2, 1), can be a factor about 8 larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface small. The results obtained clarify the existence of a relation between spindown and the oscillation amplitude. Finally, we propose a qualitative model for the explanation of the phenomenology of intermittent pulsars. The idea is that stellar oscillations, periodically excited by star glitches, can create relativistic winds of charged particles because of the additional electric field. When the stellar oscillations damp, the pulsar shifts below the death line in the P-B diagram, thus entering the OFF invisible state of intermittent pulsars.

Properties of differentially rotating neutron stars

Kucaba M , Snopek A, Gondek-Rosinska D, Villain L, Ansorg M

Differential rotation can play an important role in e.g. the dynamical stability of the remnant formed in the coalescence of binary neutron stars. Depending on the degree of differential rotation, the masses of merging neutron stars and the stiffness of equation of state the merger remnant can collapse to a black hole or be temporarily supported by rotation against collapse. We shall present a new investigation on the structure of differentially rotating neutron stars, using a well tested, multi-domain relativistic spectral code.The high level of accuracy and stability of the code enable us to calculate various types of configurations, which were not considered in previous work, mainly due to numerical limitations. We study the effects of an equation of state and the degree of differential rotation on properties of rotating neutron stars, mainly focusing on their different types of solutions and on the indicators of their stability like the Kerr parameter or the ratio of the kinetic to the gravitational potential energy.

Oscillations of maturing neutron stars, accounting for thermal effects and the crust

Krueger C

We study the spectrum of compact stars in the framework of General Relativity, where our focus lies in developing a formalism which comprises the many different physical properties of a neutron star (according to the current state-of-the-art) and allows us to use the most up-to-date data straightaway. Our results represent the first step in this direction. We use a modern, realistic equation of state including composition gradients and density discontinuities. We evolve the temperature distribution in the interior of the neutron star in time and use the temperature profiles in order to account for thermal pressure in the perturbations. We use the temperature evolution to study the effect of thermal pressure on the different oscillation modes over time. Secondly, we simulate the formation of the solid part of the crust, for which we have derived a new set of perturbation equations and we extract the frequencies of the crustal shear modes.

Quasi-normal modes of a relativistic superfluid neutron star

Gualtieri L

Using a method recently developed to describe superfluid neutron stars in general relativity including finite temperature effects, we determine how superfluidity affects the quasi-normal mode spectrum of the star. Solving a coupled system of differential equations, we consistently compute the frequency and the

61 gravitational damping time of the quasi-normal modes. We find a new family of modes, associated to oscillations of the chemical potential imbalance, and a shift of the f-mode and of the p-modes.

How to test kerr hypothesis

Lukes-Gerakopoulos G

We expect that a compact object with a mass greater than three solar masses is a Kerr Black hole. This conjecture is known as the Kerr hypothesis, and it has yet to be confirmed by observational data. In this talk we are going to discuss some of the proposed methods to check this hypothesis.

The location of resonant orbits in the kerr spacetime

Brink J , Geyer M, Hinderer T

The location of resonant orbits in the Kerr metric have observable astrophysical implications for extreme mass ratio inspirals (EMRI) around a supermassive black hole. If during the inspiral, the longitudinal and radial orbital frequencies of the inspiralling object become resonant a rapid transfer of energy and angular momentum may take place. As a result an observable phase shift in the emitted gravitational radiation may be observed. The location of resonant orbits also indicate which geodesic orbits are most likely to become chaotic in the event that the central object is non-Kerr or if the orbiting particle has non-zero spin. In this paper we completely characterize the location and properties of all resonant orbits in the Kerr spacetime for all possible values of mass, spin and orbital parameters. We give a number of easily evaluated formula for the spatial and frequency dependence of this phenomenon that will simplify the task of making qualitative statements about the system should resonant behaviour be observed. We comment of the relative importance of the various resonant orbits and the implications of their location in the strong field regime.

Testing the kerr-nature of black hole candidates

Bambi C

Astrophysical black hole candidates are thought to be the Kerr black hole predicted by General Relativity, but the actual nature of these objects has still to be verified. The Kerr black hole hypothesis can be tested by observing strong gravity features and check if they are in agreement with the predictions of General Relativity. In this talk, I will show how the already available X-ray data constrain possible deviations from the Kerr geometry around stellar-mass black hole candidates. These bounds are obtained by combining the study of the disk’s thermal spectrum, the analysis of the relativistic K-alpha iron line, and the estimate of jet powers.

62 Testing general relativity with accretion flows around sgr a*

Straub O, Vincent F, Gourgoulhon E, Some C

We propose a new test of general relativity that relates to one of the fundamental questions in astro- physics: How can we know whether a dark and compact object is indeed a black hole as predicted by Einstein’s theory of general relativity? How easily can black holes be mimicked by exotic objects or other space-time geometries? To answer these questions we are going to simulate numerically the direct environment of various dark and compact objects, with special attention to the properties of the compact core region of our own galaxy, the Milky Way. We calculate the images of their silhouettes as they will be perceived by an observer on Earth. By calculating (i) the images of compact objects other than “classi- cal” black holes and (ii) objects that emerge from gravitational theories other than general relativity we aim at elaborating a set of criteria according to which it will be possible to discern the different models. The ultimate goal is the comparison with images of the black hole silhouettes observed by near-future high angular resolution Very Long Baseline Interferometry. A catalogue of different images will facilitate the analysis and interpretation of such data and enable us to confirm or refute the presence of a general relativistic black hole in the centre of our galaxy.

Tests of general relativity in the strong gravity regime based on x-ray polarimetric observations of black holes

Krawczynski H

In this contribution we report on a study that explores the possibility to use X-ray spectropolarimetric observations of black holes in X-ray binaries to distinguish between the Kerr metric and the phenomeno- logical metrics introduced by Johannsen and Psaltis (2011) (which are not vacuum solutions of Einstein’s equation) and thus to test the no-hair theorem of GR. To this end, we have developed a numerical code that calculates the radial brightness profiles of accretion disks and parallel transports the wave vector and polarization vector of photons through the Kerr and non-GR spacetimes. We used the code to predict the observational appearance of GR and non-GR accreting black hole systems. We find that the predicted energy spectra and energy dependent polarization degree and polarization direction do depend strongly on the underlying spacetime. However, for large regions of the parameter space, the GR and non-GR metrics lead to very similar observational signatures, making it difficult to observationally distinguish between the two types of models.

Observing massive black holes with extreme-mass-ratio bursts

Berry C , Gair J

The centres of galaxies harbour massive black holes of 104 − 1010 solar masses. These are observed to have masses closely correlated to their hosts’ properties, suggesting a shared evolutionary history. An exciting means of probing the properties of these massive black holes is with gravitational waves. Extreme-mass-ratio bursts are a gravitational wave signal produced when a solar mass companion passes close to a massive black hole on a highly eccentric orbit. Bursts are an unexplored tool for gravitational wave astronomy. We shall discuss an approximate means of modelling bursts, and assess the accuracy of parameter estimation for bursts from nearby massive black holes. In the best case scenario, we would be able to measure the mass and spin of the Galaxy’s massive black hole to one part in 104.

63 When can gravitational-wave observations distinguish between black holes and neutron stars?

Hannam M , Brown D, Fairhurst S, Fryer C, Harry I

Gravitational-wave observations of compact binaries have the potential to uncover the distribution of masses and angular momenta of black holes and neutron stars in the universe. The binary components’ physical parameters can be inferred from their effect on the phasing of the gravitational-wave signal, but a partial degeneracy between the components’ mass ratio and their angular momenta limits our ability to measure the individual component masses. At the typical signal amplitudes expected by the Advanced Laser Interferometer Gravitational-wave Observatory (signal-to-noise ratios between 10 and 20), we show that it will in many cases be difficult to distinguish whether the components are neutron stars or black holes. We identify when the masses of the binary components could be unambiguously measured outside the range of current observations. We also identify those configurations that could be unambiguously identified as black-hole binaries, and show how the observation of an electromagnetic counterpart to a neutron-star–black-hole binary could be used to constrain the black-hole spins.

Nodal precession of orbits about rotating strange stars

Rosinska D, Kluzniak W, Stergioulas N, Wisniewicz M

We compute the epicyclic frequencies of nearly circular orbits around rotating strange stars. The MIT bag model is used to model the equation of state of quark matter and the uniformly rotating stellar configurations are computed in full GR. The vertical epicyclic frequency, and the related nodal precession rate of inclined orbits, are very sensitive to the oblateness of the rotating star. For slowly rotating stellar models of about 1.4 solar mass strange stars, the sense of the nodal precession changes at a certain rotation rate. At lower stellar rotation rates the orbital nodal precession is prograde, as it is in the Kerr metric, while at higher rotation rates the precession is retrograde, as it is for Maclaurin spheroids. Thus, qualitatively, the orbits around rapidly rotating strange stars are affected more strongly by the effects of stellar oblateness than by the effects of GR.

Observable predictions for two models of quasi-periodic oscillations in microquasars

Vincent F , Abramowicz M, Mazur G, Varniere P, Meheut H, Paumard T

This talk will present observable predictions for two models of microquasars’ quasi-periodic oscillations (QPOs): - the deformed torus model, a more evolved counterpart of the famous resonance QPO model by Abramowicz & Kluzniak (2001). This model assumes that QPOs are due to deformations of a slender accretion torus around a Kerr black hole. - the Rossby wave instability model (Tagger & Varniere, 2006), that assumes QPOs are due to the triggering of the hydrodynamical Rossby wave instability in the microquasar’s accretion disk. I will present general relativistic ray-tracing simulations of QPOs light curves and power spectral densities that demonstrate the ability of these two models to account for QPOs observed data. I will highlight the ability of both models to imply specific observable predictions that may be tested by future-generation instruments. I will address the question of the ability of the LOFT instrument to differenciate these models by showing simulated LOFT data for the two models.

64 On the existence of spherical accretion flows

Chaverra Sanchez E, Sarbach O

We analyze the radial accretion of matter onto a static, spherically symmetric black hole background. Although our assumption is strong in that it implies the hole to be non-rotating, we do not necessarily assume the spacetime metric to be the Schwarzschild one. Therefore, our discussion includes black hole metrics that could occur in alternative theories of gravity, or as solutions of Einstein’s field equations in the presence of matter fields, like dark matter, for instance. Modeling the ambient matter surrounding the black hole by a relativistic perfect fluid with an equation of state satisfying specific conditions, we reformulate the accretion problem as a dynamical system. We demonstrate that our assumptions on the metric and the fluid imply the existence of a unique critical hyperbolic point of this system. Physically, the critical point is the sonic point, where the flow’s velocity, as measured by a static observer, is equal in magnitude to the local sound speed. Generalizing previous work by Michel we prove that for a given particle density number at infinity, there exists a unique radial, steady-state accretion flow which is regular at the horizon.

Gravitational waves from oscillon preheating

Zhou S

Oscillons are long-lived, localized excitations of nonlinear scalar fields. They may be copiously pro- duced in the preheating phase after inflation, leading to a possible oscillon-dominated epoch in the early Universe. We investigate the stochastic gravitational wave background generated during this phase. Gravitational wave production during the oscillon-dominated phase itself is small, but a significant back- ground is generated as the oscillons form. In contrast to the spectrum produced during other preheating scenarios, the gravitational wave power spectrum produced has distinct multiple peaks, imprinted by forming of spherically symmetric oscillons, as opposed to the single broad peak generated by other preheating mechanisms.

Highly eccentric kozai mechanism and gravitational wave observation for neutron star binaries

Seto N

The Kozai mechanism for a hierarchical triple system could reduce the merger time of inner eccentric binary emitting gravitational waves (GWs), and has been qualitatively explained with the secular theory that is derived by averaging short-term orbital rotations. However, with the secular theory, the minimum value of the inner pericenter distance could be artificially blocked by the back-reaction of GW emission. Compared with traditional predictions, the actual evolution of an eccentric inner binary could be accom- panied by (i) a higher characteristic frequency of the pulse-like GWs around its pericenter passages, and (ii) a larger residual eccentricity at its final inspiral phase. These findings would be important for GW astronomy with the forthcoming advanced detectors.

65 Poster session

On cosmic strings, causality violation and brane world models

slagter R

At first glance, it seems possible to construct in general relativity theory causality violating solutions. The most striking one is the Gott spacetime. Two cosmic strings, approaching each other with high velocity, could produce closed time like curves. One considers the effective spinning cosmic string in the (2+1)-dimensional space time by omitting the dz-term in the metric. The resulting gravitating spinning point-particle has interesting local properties and the model could serve as a toy-model in constructing a quantized theory. However, the treatment of the Killing vectors seems to be unsatisfactory, since the stationary space time is equivalent (after a complex transformation) to a cylindrical space time, where gravitational waves will be involved. Also, the treatment of the 4-dimensional cosmic string as a tiny and very long cylinder, where the mass is concentrated on the z-axis, will give rise to some unusual behavior. After all, the cosmic string is the result of a U(1)-gauge model. On a 5-dimensional warped space time, it seems possible to construct closed time like curves and the pathology in lowering the dimension of the space time does not arise. There is, however, a side effect. From the effective four-dimensional field equations on the brane, it follows that no asymptotic conical space time is found, so no angle deficit as in the 4D counterpart model. If we would live in a (3+1)-dimensional brane, then no lensing effect of cosmic strings will be observed.

Electrodynamic system of earth in astrophysical investigation

Grunskaya L, Isakevich V, Rubay D

Since 2000 there has been working the united system of monitoring of electrical and geomagnetic fields of ELF range of the atmosphere boundary surface layer at the spaced apart stations: Vladimir State physical experimental ground; the station of RAS Institute of Sun and Earth physics at Lake Baikal; the station in Paratunka (Kamchatka); the station in Obninsk. There has been developed a programme-analytical system (PAS) to investigate signal structures in spectral and time series, caused by geophysical and as- trophysical processes based on the method of eigen vectors. There were discovered frequencies in the elec- trical and geomagnetical field of ELF range with PAS, which coincide with the frequency of gravitational wave radiation of a number of double stellar systems. In the electrical and geomagnetic field there was discovered a specific axion frequency VA=0.5*10-5 Hz belonging to the ELF range which was predicted by the theory. Report is based on the papers: 1.Grunskaya L.V.,Efimov V.A., Isakevich V.V.,Zakirov A.A. Experimental investigations of the interaction between the ELF Earth electromagnetic fields and astrophysical processes. //American Institute of Physics AIP Conf. Proc.2010.-V.1206.-p.455-461. 2. Grunskaya L.V. Using the basis of eigen vectors of covariance matrix for exposing time series complex periodical components./ L.V.Grunskaya, V.V.Isakevich, L.T.Sushkova, A.A.Zakirov//Electromagnetic waves and electronic systems. Radio Engineering-2010 #10 p.24-28

Limb -effect of rapidly rotating stars

Morcos A

Kerr metric is used to study the limb-effect phenomenon for an axially rotating massive stars. The limb effect phenomenon is concerning by the variation of the red shift from the center to the limb of star.

66 This phenomenon has been studied before for the sun. The solar gravitational field is assumed to be given by Schwarzschild and Lense-Thirring fields. In this trial, a study of the limb effect for a massive axially symmetric rotating star. The line of site inclination and the motion of the observer are taken into consideration to interpret a formula for this phenomenon using a general relativistic red–shift formula. A comparison between the obtained formula and previous formulae is given.

Some aspect of a cosmological black hole

Taghizadeh Firouzjaee J , Mansouri R

Application of concepts like black hole and event horizon in cosmological context are not trivial, as has been shown in the last decade. We introduce special solutions of the LTB family representing collapsing over-dense regions. The result shows how a dynamical black hole evolves within the FRW universe, its decoupling from the expanding parts of the model, the structure of its space-like apparent horizon, the limiting case of the dynamical horizon tending to a slowly evolving horizon, and the decreasing mass in-fall to the black hole. Using this cosmological black hole model, we have calculated the test particle geodesics within the structure for different general relativistic masses in order to obtain the velocity profile of stars or galaxies. Defining a Newtonian mass based on the classical dynamical relations, it turns out that the Misner-Sharp quasi-local mass is almost equal to the Newtonian one. The other mass concepts, however, may differ substantially.

Spin down of rotating strange stars

Ahmedov B, Fayzullayev D

We have shown that in general relativity slow down of the pulsar rotation due to the magnetodipolar radiation is more faster for the strange star with compared to that for the neutron star of the same mass. Comparison with astrophysical observations on pulsars spindown data may provide an evidence for the strange star existence and, thus, serve as a test for distinguishing it from the neutron star. The rotational evolution of rotating magnetized strange stars with plasma magnetosphere has been also studied.

Mapping the milky way using its rotation curve without the need for dark matter or alternative theories of gravity

Magalhaes N , Cooperstock F

We present remarkable fits to the rotation curves of three galaxies obtained with an approach that does not demand any modified theory of gravitation or to hypothesize the existence of dark matter. Only classical general relativity was applied. We used the coefficients of the fits to determine the mass densities as functions of galactocentric distances and heights, calculated the galaxies’ masses and determined the first approximation to their morphologies, generating a first order map of their mass distributions. The galaxies we investigated were the Sunflower galaxy (NGC 5055), Andromeda (NGC 0224) and the Milky Way. To our knowledge, this is the first time that such a theoretical mapping has been performed. It is particularly useful in the case of Milky Way, which is harder to map astronomically from our position within.

67 Shadow of kerr-taub-nut black hole

Abdujabbarov A

The shadow of a rotating black hole with nonvanishing gravitomagnetic charge has been studied. It was shown that in addition to the angular momentum of black hole the gravitomagnetic charge term deforms the shape of the black hole shadow. From the numerical results we have obtained that for a given value of the rotation parameter, the presence of a gravitomagnetic charge enlarges the shadow and reduces its deformation with respect to the spacetime without gravitomagnetic charge. Finally we have studied the capture cross section for massive particles by black hole with the nonvanishing gravitomagnetic charge.

Acceleration of particles by black hole with gravitomagnetic charge immersed in magnetic field

Abdujabbarov A

The collision of test charged particles in the vicinity of an event horizon of a weakly magnetized non- rotating black hole with gravitomagnetic charge has been studied. The presence of the external magnetic field decreases the innermost stable circular orbits (ISCO) radii of charged particles. The opposite mech- anism occurs when there is nonvanishing gravitomagnetic charge. For a collision of charged particle moving at ISCO and the neutral particle falling from infinity the maximal collision energy can be de- creased by gravitomagnetic charge in the presence of external asymptotically uniform magnetic field.

The model of dark galactic halo based on equilibrium distribution function

Gladush V

The model of galactic halo as a system of the collisionless small neutral particles from the standpoint of kinetic theory is considered. For the equilibrium system with the use of Maxwell-Boltzmann distribution we obtained results which explain the observed flat rotation curve. These results practically coincide with the results of equilibrium spherical gas cloud model in Newtonian gravitation with linear state equation.

Shocks in chaplygin gas accretion

John A, Maharaj S

Studies of the accretion of dark matter onto intermediate mass black holes (IMBHs) suggest a finite lower bound for the dark matter sound speed. We consider the generalised Chaplygin gas (GCG) as a collisional dark matter candidate and study its steady, spherically symmetric accretion onto a Newtonian star. We obtain analytic expressions for the sonic radius and mass accretion rate. A shock front is anticipated as the supersonic gas impacts upon the hard stellar surface. We obtain and solve the Rankine-Hugoniot equations for the post-shock pressure, density and Mach number. The thermodynamic feasibility of weak post-shock states is analysed.

68 Proto-neutron stars evolution and gravitational wave emission

Fortin M , Leonardo G, Ferrari V, Benhar O

Just after their birth in a supernova explosion, the evolution of proto-neutron stars (PNSs) is dominated by dynamical phenomena (shock waves, neutrino winds, ...). After 200 ms, it can be considered as quasi- stationary and be modelled by a sequence of equilibrium configurations. At first, the core undergoes a phase of deleptonization due to the emission of high-energy neutrinos that are trapped in the PNS. As a result, the star is heated up to a temperature of several tens of MeV during few tens of seconds. Then the energy of the neutrinos decreases and the PNS cools down. After 50 s, the PNS becomes transparent to neutrinos that freely escape and a neutron star is born. Thus, during the quasi-stationary evolution the PNS emits a large amount of its energy in the form of neutrinos and to a lesser extent in the form of gravitational waves associated with its oscillation modes. The properties of these modes are determined by the thermal and chemical evolutions and are driven by the diffusion of neutrinos inside the PNS. I will present an ongoing project dealing with the modelling of the neutrino diffusion in the PNS during the quasi-stationary evolution. It aims to consistently describe the thermal and chemical evolutions using up-to-date descriptions of the properties of nuclear matter at high densities. As a result, the influence of the nuclear properties on the oscillation modes and on the associated gravitational wave emission can be assessed.

Equations of state for tolman vii solutions and models of compact stars

Raghoonundun A, Hobill D

While the Tolman VII (T7) solution to the Einstein equations with a spherically symmetric matter distribution has been known since 1939, only recently has it been discussed in terms of its ability to describe a realistic astrophysical object. Extending the analysis to both the ”natural” (with vanishing surface density) and ”self-bound” (with non-zero surface density) cases, we have been able to show that there are significant differences between the equations of state (EOS) in the two cases when causality conditions are applied. In the former case, the EOS approximates that of a sequence of polytropes, while in the latter case the EOS is more exotic. We compute measurable quantities such as masses and radii for these compact objects, and show that these are consistent with recently observed values for neutron stars. Furthermore, we test the stability under linear perturbations of these new solutions as applied to compact astronomical objects, and show that parameter values (radius, central density, compactness, and adiabatic index) for which T7 is stable exists.

69 Constraints on the reissner–nordstrom metric for the black hole at the galactic center

Zakharov A

Theories with extra dimensions admit astrophysical objects (supermassive black holes in particular) which are rather different from standard ones. People proposed tests which may help to discover signatures of extra dimensions in supermassive black holes since the gravitational field may be different from the standard one in the GR approach. Recently, Bin-Nun (2010) discussed an opportunity that the black hole at the Galactic Center is described by the tidal Reissner– Nordstrom metric which may be admitted by the Randall–Sundrum II braneworld scenario. Bin-Nun suggested an opportunity of evaluating the black hole metric analyzing (retro-)lensing of bright stars around the black hole in the Galactic Center. Doeleman et al. evaluated a size of the smallest spot for the black hole at the Galactic Center with VLBI technique in mm-band (Doeleman et al. 2008). Theoretical studies showed that the size of the smallest spot near a black hole practically coincides with shadow size because the spot is the envelope of the shadow. Measurements of the shadow size around the black hole may help to evaluate parameters of black hole metric. We derive an analytic expression for the black hole shadow size as a function of the tidal charge for the Reissner– Nordstrom metric. We conclude that observational data concerning shadow size measurements are not consistent with significant negative charges.

Gravitational waves after pulsar glitches

Kim J, Lee H , Kim H

We investigate oscillation amplitudes of modes and their frequencies induced by pulsar glitches using our new numerical code based on pseudo-Newtonian approach. We imposed two kinds of perturbations that could mimic the pulsar glitch theories i.e., change of moment of inertia due to the star quakes or angular momentum transfer by vortex unpinning at crust-core interface. We also the characteristic amplitude of gravitational wave using quadrupole moment in numerical simulation. We made detailed estimations for the gravitational wave amplitudes for different mass and perturbation. One of the interesting features of our calculation is the vortex unpinning model excites the inertial mode in quadrupole moment quite effectively. Although the amplitude is not very strong due to its fairly low frequency, its frequency falls at the most sensitive region in LIGO and its damping time is regarded as longer than other modes. It also may be able to evolve into the non-axisymmetric r -mode which can give much stronger strain.

Post-mortem of a binary neutron star merger

Li T , Agathos M, Walter D, Chris V, Salvatore V

Gravitational waves from binary neutron star mergers encode information regarding the neutron star equation of state. Existing literature, which is mainly based on Fisher Matrix calculations or waveform comparisons for single sources, suggests that the upcoming Advanced LIGO-Virgo network can only discern extreme equations of state. We present the first Bayesian investigation of the detectability of the neutron star equation of state by the Advanced LIGO-Virgo network. Bayesian inference allows for the combination of information from multiple sources. We simulate binary neutron star mergers with tidal contributions in the gravitational wave phase and use the framework of Bayesian model selection to rank a particular set of three competing equations of state - a hard, a moderate, and a soft one. We show that only few tens of sources are required to correctly rank these three equations of state. These results suggest that the Advanced LIGO-Virgo network can quickly rule out certain classes of equations of state and thereby aid future research in neutron star physics.

70 Thermal evolution of a radiating anisotropic spherical configuration with non-local equation of state

Becerra L, Hernandez H, Nunez L

We study the collapse of dissipative anisotropic spherical matter configuration having NonLocal Equation of state. This particular type of equation of state has been successfully used to represent ultra-dense com- pact objects and it describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. The collapsing scenarios were considered in two regimes: slow contraction approximation (when changes of the system take place on a time scale that is very long compared to the hydrostatic time scale) and with no approximation at all. The dissipation and the associated behaviour of the temperature profile of the evolving configurations were investigated within the framework of causal thermodynamics (Israel- Stewart and the Cattaneo equations). We have found that previous reported thermal effects, such as thermal peeling, (the exterior layers of the configuration escape from gravitational attraction while the interior layers are attracted) are also present for non-local configurations with different density distri- bution and for some particular dissipations profiles. We show that the Cattaneo approximation for the Israel-Stewart equation is enough to describe the temperature gradient in both collapsing regimes for non-local distribution of matter.

The effects of the equation of state and differential rotation on the maximum mass of neutron stars

Studzi´nskaA, Kucaba M, Gondek-Rosinska D, Villain L, Ansorg M

Binary neutron star merger lead to the formation of a massive differentially rotating neutron star or to the prompt collapse to a black hole. The maximum mass of a differentially rotating remnant is crucial for distinguishing between these two final objects. We study the effect of an equation of state and on the maximum mass of neutron stars for broad ranges of gravitational masses, degrees of differential rotation. We numerically construct stellar models using a highly accurate relativistic code based on a multi-domain spectral method (Ansorg, Gondek-Rosinska, Villain, 2009). We found that the maximum allowed mass of differentially rotating neutron star has the highest value for moderately stiff equation of state and moderate degrees of differential rotation. In comparison to non-rotating models, differential rotation can increase maximum allowed mass of neutron star even up to 4 times. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.

Vertical stability of equatorial circular orbits in relativistic razor-thin disks

Vieira R, Ramos-Caro J, Saa A

We present a rigorous treatment for the vertical stability of equatorial circular orbits in relativistic razor- thin disks surrounded by static, axially symmetric 3D matter distributions. The analysis is consistent with the theory of distributional energy-momentum tensors in curved spacetimes and takes into account the delta-like singularity explicitly. Jointly with the usual radial stability criterion, the vertical stability condition presented ensures Lyapunov stability of the corresponding circular orbit. We also obtain an approximate third integral of motion for off-equatorial, quasi-circular orbits crossing the disk. This last expression describes the envelope of nearly-equatorial orbits in the system’s meridional plane. Our results give a consistent way to obtain the ISCO’s radius in razor-thin accretion disk models and also correct previous analyses existing in the literature, which do not consider the delta-like singularity and therefore must be revisited. The present research is an extension of our recent work on Newtonian razor-thin disks.

71 Upper limits of particle emission from high-energy collision and reaction near a maximally rotating kerr black hole

Harada T , Nemoto H, Miyamoto U

The center-of-mass energy of two particles colliding near the horizon of a maximally rotating black hole can be arbitrarily high if the angular momentum of either of the incident particles is fine-tuned, which we call a critical particle. We study particle emission from such high-energy collision and reaction in the equatorial plane fully analytically. We show that the unconditional upper limit of the energy of the emitted particle is given by 218.6% of that of the injected critical particle, irrespective of the details of the reaction and this upper limit can be realized for massless particle emission. The upper limit of the energy extraction efficiency for this emission as a collisional Penrose process is given by 146.6%, which can be realized in the collision of two massive particles with optimized mass ratio. Moreover, we analyze perfectly elastic collision, Compton scattering, and pair annihilation and show that net positive energy extraction is really possible for these three reactions. The Compton scattering is most efficient among them and the efficiency can reach 137.2%. On the other hand, our result is qualitatively consistent with the earlier claim that the mass and energy of the emitted particle are at most of order the total energy of the injected particles and hence we can observe neither super-heavy nor super-energetic particles.

I love q forever

Maselli A

Coalescing binaries are among the most promising sources of gravitational waves for the new generation of terrestrial and space interferometers. Moreover they have been suggested as a possible explanation of short gamma-ray burst. Tidal interactions occurring in the last phases of these systems, can cause the neutron star disruption and are equation of state dependent: detection of the emitted gravitational signal may hence provide useful information on the stellar internal structure. In this talk we present a new semi-analytical approach to describe tidal interactions in black hole- neutron star or neutron star-neutron star binaries, based on the post-Newtonian expansion and the Affine approximation, showing how this model allows to derive the neutron star deformation properties. In particular, we study the evolution of the neutron star tidal deformability during the inspiral, evaluating the impact of its change for a future gravitational wave detection. Moreover, we determine the range of validity of the I-Love relation between the tidal love number and the star momentum of inertia, up to the merging phase. We also discuss the possibility of using a new relation, involving the Love number and the star compactness, to measure the neutron star radius with an accuracy 10 % from gravitational-wave observations.

exact general relativistic lensing versus thin lens approximation: the crucial role of the void

Taghizadeh Firouzjaee J , mansouri R, parsi mood M

We have used an exact general relativistic model structure within a FRW cosmological background based on a LTB metric to study the gravitational lensing of a cosmological structure. The deviation angle calculated by the integration of the geodesic equations for different density profiles of the model structure was then compared to those of the corresponding thin lens approximation. Using the familiar NFW density profile, it is shown that independent of the truncation details the thin lens approximation differ substantially from the exact relativistic calculation. The difference in the deflection angle for different impact parameters may be up to about 30 percent. However, using the modified NFW density

72 profile with a void before going over to the FRW background, as required by an exact general relativistic model, the thin lens approximation coincides almost exactly with the general relativistic calculation.

Keplerian rotation curves vs central mass in accretion disk systems.

Pir´ogM

We have investigated accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation - its rotational frequency is larger than that given by the well known strictly Keplerian formula that takes into account the central mass only. Thus determination of central mass in systems with massive disks requires great care - the strictly Keplerian formula yields only an upper bound. The effect of self-gravity depends on geometric aspects of disk configurations. I would like to show how we could estimate the ratio of the central to disk mass and clarify how the estimate, based on Keplerian rotational curves, is reliable.

Quantised vortices and mutual friction in relativistic superfluids.

Wells S, Andersson N

Superfluidity is key to our understanding of neutron stars. In order to model them as accurately as possible, we need to describe them in relativity. In the Newtonian framework, the superfluid equations can be derived by taking a quantised vorticity vector as the starting point. We develop this approach in relativity and produce an argument analogous to the Newtonian formulation. Adding a second component to the system (the normal fluid) we obtain the first description of the vortex-mediated mutual friction in the relativistic case.

Quadrupole moments of rotating compact stars

Urbanec M , Miller J, Stuchlik Z

Results of neutron star and strange stars modelling are present. We calculate parameters of rotating stars such as gravitational mass M, angular momentum J and quadrupole moment Q within the slow- rotation (Hartle-Thorne) approximation. We demonstrate that parameter QM/J 2 ,if plotted against compactness, is almost independent on neutron star equation of state and differ significantly from the one calculated for strange stars.

Trapping of neutrinos in maximally compact non-rotating stars

Hladik J , Stuchlik Z, Urbanec M

We study the phenomenon of trapping of neutrinos in the strong gravitational fields of maximally massive compact stars described by the physically relevant equation of state supposed by Rhoades and Ruffini. We computed coefficients describing the influence of this process on global and local neutrino luminosity. It can be assumed that presented results could serve as approximate upper limit achievable in less massive stars. Despite the absence of neutrino trapping effect in compact stars described by the commonly used EOS (SkI, SLy, ...) we expect its relevancy in strange stars and Q-stars.

73 Joint session B2 and B4: Approximate solutions to Einstein equations, Methods and Applications’

Oral session

Numerical simulations of binary black holes: applications enabled by many simulations

Pfeiffer H

Recently, the SXS-collaboration collaboration has succeeded in computing about 100 binary black hole (BBH) coalescence waveforms. These waveforms include a very long inspiral phase (some exceeding 60 cycles) and are of exquisite accuracy. The configurations simulated include extreme regions of the BBH parameter space like nearly extremal spins, high mass-ratios, and strongly precessing systems. This talk reports on applications of these waveforms to study strong field gravity and aid gravitational wave astronomy, in particular post-Newtonian comparisons and construction of template banks for BBH waveforms.

Nearly extremal black-hole spin in numerical simulations of compact binaries

Lovelace G

Merging black-hole/black-hole (BHBH) and black-hole/neutron-star (BHNS) binaries are among the most promising sources for advanced gravitational-wave detectors, and BHNS binaries are also one possible engine for short, hard gamma-ray bursts. Because all analytic approximations fail near the time of merger, the behavior of the curved spacetime (including the emitted gravitational waves) and of neutron star matter during and after tidal disruption can only be predicted using fully relativistic numerical simulations. Astrophysical black holes could have spins that are nearly extremal (i.e. nearly as rapid as possible), but to date numerical simulations containing nearly extremal black holes remain challenging. In this talk, after briefly summarizing these challenges, I will present results obtained using the Spectral Einstein Code for BHBH and BHNS mergers with nearly extremal black-hole spins. The behavior of the spacetime and matter both depend strongly on the black-hole spin, leading to behavior that deviates from extrapolations of simulations with lower black-hole spins.

74 Investigations into the origin of ringdown mode structure

Khan S, Hannam M

Recent work demonstrated a relationship between the parameters of a black-hole-binary system and the relative amplitudes of the ringdown modes of the final black hole (Kamaretsos et al 2012). I will present results of attempts to produce a simple physical model of the observed mode structure

Accuracy and convergence of moving puncture binary black hole simulations

Husa S, Hannam M, P´urrerM, Johnson McDaniel N, Reisswig C, Pollney D, Ruiz M, Va˜noVi˜nualesA

We present a detailed study of the accuracy and convergence of numerical binary black hole simulations in the context of finite difference techniques and the moving puncture framework. We analyze separately the accuracy in the spatial and temporal discretizations, and find that the significance of the temporal discretization error varies significantly over the parameter space. We also discuss different ways to quantify and interpret phasing accuracy in the context of gravitational wave data analysis.

The Perils of Analytic Continuation

Woodard R

Analytic continuation is a wonderful technique in physics but it fails to reproduce power law divergences. This is the origin of the famous “automatic subtraction” of dimensional regularization and zeta function regularization, but it occurs as well for analytic continuation from Euclidean space and for analytic continuation in the mass-squared. What to make of an automatic subtraction depends upon the physics behind the divergence. Ultraviolet divergences would be subtracted by renormalization, so an automatic subtraction merely spares one the trouble of working out the counterterm and making the subtraction. The case of infrared divergences is very different. They signal an error in the physical question being posed and it is completely incorrect to subtract them. I show that this error is behind claims that tachyonic scalars on de Sitter background have de Sitter invariant propagators. I also comment on the relevance to claims that the graviton propagator is de Sitter invariant.

Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries

Pan Y

Accurate analytical modelling of coalescing compact binaries is essential to detect gravitational waves and extract astrophysical information with Advanced LIGO and Virgo detectors. Although substantial progress has been made in the past few years to model waveforms emitted by spinning, non-precessing black-hole binaries, precessing waveform models are still lacking. Working within the analytical effective- one-body (EOB) approach, we propose a prescription to build precessing waveforms from non-precessing ones and discuss how the resulting EOB waveforms compare with the ones produced in numerical- relativity simulations.

75 Spinning, non-precessing black-hole binaries and their effective-one-body modeling

Taracchini A, Pan Y, Buonanno A, Hughes S, Khanna G, Barausse E, Boyle M, Chu T, Lovelace G, Pfeiffer H, Scheel M

I will discuss the modeling of inspiral-merger-ringdown gravitational waveforms radiated by non-precessing, spinning black-hole binaries for any mass ratio within the effective-one-body (EOB) approach. In the comparable-mass limit, the EOB waveforms are calibrated to highly-accurate numerical-relativity wave- forms produced by the Spectral Einstein Code. In the extreme-mass-ratio limit, the EOB waveforms are improved using numerical waveforms produced via the Teukolsky equation, including also black-hole absorption effects.

The overlap of numerical relativity, perturbation theory and post-newtonian theory in the binary black hole problem

Le Tiec A

Inspiraling and coalescing binary black holes are among the most promising sources of gravitational radiation to be detected by current ground-based interferometers and future space-based antennas. The detection and analysis of the signals from these highly relativistic sources require very accurate theoretical predictions, for use as gravitational-wave templates to be compared to the output of the detectors. The orbital dynamics and gravitational-wave emission of such systems can be investigated using a variety of approximation schemes and numerical methods in General Relativity: the post-Newtonian formalism, black hole perturbation theory, numerical relativity, and the effective-one-body framework. The last years have seen an increasing amount of activity at the multiple interfaces of all of these analytical and numerical techniques. I will review this recent work, emphasizing the use of coordinate invariant relations to perform meaningful comparisons. Some highlights include (i) the remarkable agreement between the predictions of the various methods, and (ii) the surprising observation that perturbation theory may turn out to be useful in the modeling of comparable-mass binary black holes.

Black hole motion on a non-uniform scalar field in scalar-tensor theories

Gualtieri L

Scalar-tensor theory is one of the most interesting and promising extensions of general relativity. Using analytical modelling and fully relativistic numerical simulations, we have studied the behaviour of black holes on a non-trivial scalar field profile, finding that in presence of acceleration (as for instance in the case of a coalescing black hole binary), scalar radiation is emitted.

Gravitational self-force from curvature scalars

Merlin C , Barack L

The standard formulation of the gravitational self-force in Kerr spacetime requires as input the metric perturbation in the Lorenz gauge. The latter may be obtained numerically using time-domain evolution of the linearized Einstein equations, which, alas, is computationally expensive. Here we describe a

76 new framework for self-force calculations, in which the required input are curvature scalars obtained by solving Teukolsky’s equation. Our formulation translates to a new mode-sum formula for the self- force in a locally-Lorenz gauge, with modified regularization parameters. We derive the new parameters analytically, and present an end-to-end numerical implementation of the method for circular orbits in Schwarzschild geometry. The method offers a computationally efficient route to the self-force problem in Kerr.

Overspinning a kerr black hole

Colleoni M , Barack L

The scenario of a particle captured by a nearly extremal Kerr black hole has been proposed as a challenge to weak cosmic censorship. It is recognized that a reliable analysis of this scenario must take into account the full effect of the gravitational self-force acting on the particle. We revisit the problem, now that computational tools for the self-force are becoming available. As a preparatory step, we identify the full parameter-space domain where overspinning is achieved when the self-force is ignored (this extends and refines previous work). Interestingly, we find (working at leading order in the mass ratio) that overspinning can only be achieved by particles coming from infinity. We outline the program to obtain the self-force data necessary as input for a reliable analysis of the problem.

Effective field theory approach to love numbers of black holes

Kol B, Smolkin M

Black holes exhibit deformations in the presence of external gravitational field. If the size of the black hole is much smaller than the characteristic length scale over which the external field varies, then these deformations can be characterized by a set of dimensionless parameters (Love numbers) that measure susceptibility of the black hole to tidal forces. In my talk I will argue that such Love numbers naturally emerge in the Effective Field Theory approach and discuss various ways to evaluate them.

77 B2 - Numerical relativity and astrophysical applications

Oral session

Gravitational and electromagnetic radiation from binary neutron star mergers

Palenzuela C , Lehner L, Ponce M, Liebling S, Neilsen D, Anderson M, Motl P

Our main goal is to investigate how the strongly gravitating and highly dynamical behavior of mag- netized binary neutron stars can affect the plasma in the magnetosphere in such a way that powerful electromagnetic emissions can be induced, as well as stressing its connection with gravitational waves produced by the system. Such phenomena is a natural candidate for bright (EM) and loud (GW) emis- sions, as pulsars are strong electromagnetic emitters on one hand, and merging binary neutron stars are powerful sources of gravitational radiation.

Disks and outflows from black hole-neutron star mergers: progress toward realistic microphysics and binary parameters

Duez M , SpEC C

The outcome of compact binary mergers involving one or two neutron stars can include a hot accretion disk and outflow, and this surviving nuclear matter can potentially generate electromagnetic signals to complement gravitational wave detections. In this talk, I review the application of the Spectral Einstein Code (SpEC) to neutron star systems. SpEC is now able to include full general relativity, magnetohydrodynamics, and neutrino cooling. We have recently used this code to perform simulations of the previously unexplored moderately high-mass, high-spin region of black hole-neutron star parameter space. We investigate the unbound ejecta, accretion disk, and neutrino signal produced by these mergers. SpEC has also been successfully used to model binary neutron star mergers and magnetic instabilities in protoneutron stars.

78 Binary black hole mergers in magnetized disks: simulations in full general relativity

Gold R, Farris B, Paschalidis V, Etienne Z, Shapiro S

We present results from the first fully general relativistic, magnetohydrodynamic (GRMHD) simulations of an equal-mass black hole binary (BHBH) in a magnetized, circumbinary accretion disk. We simulate both the pre and post-decoupling phases of a BHBH-disk system and both ’cooling’ and ’no-cooling’ gas flows. Prior to decoupling, the competition between the binary tidal torques and the effective viscous torques due to MHD turbulence depletes the disk interior to the binary orbit. However, it also induces a two-stream accretion flow and mildly relativistic polar outflows from the BHs. Following decoupling, but before gas fills the low-density ’hollow’ surrounding the remnant, the accretion rate is reduced, while there is a prompt electromagnetic (EM) luminosity enhancement following merger due to shock heating and accretion onto the spinning BH remnant. This investigation, though preliminary, previews more detailed GRMHD simulations we plan to perform in anticipation of future, simultaneous detections of gravitational and EM radiation from a merging BHBH-disk system.

Tidal effects in binary neutron star coalescence: numerical relativity simulations and analytical models

Bernuzzi S

Gravitational waves from coalescing neutron stars carry unique information about the star equation of state. An accurate theoretical modeling of these systems is of primary importance to extract robust data in a direct detection of gravitational waves. I will present results about tidal effects in binary neutron star coalescence and their signature in grav- itational radiation emitted. In particular, I will discuss the outcome of state-of-art numerical relativ- ity simulations and their comparison with analytical approaches like post-Newtonian method and the effective-onde-body model. Finally, I will present a new numerical relativity setup, based on the Z4c formulation and cubic-sphere AMR, to perform accurate simulations, and ongoing efforts.

General relativistic neturino-radiation hydrodynamics simulations : formulations and applications

Sekiguchi Y

We describe formulations of general relativistic neutrino-radiation hydrodynamics (GR-nRad-HD) and present our recent applications. Characteristic issues to be considered in the GR-nRad-HD are (1) em- ployment of tabularized equation of state where popular Newton-Raphson method cannot be applied in recover of the primitive variables due to poor estimates of the derivative, (2) the relativistic couplings between (a) the Lorentz factor and the rest-mass density and (b) inertia and the enthalpy, which make it difficult to adopt implicit schemes as well as complicate the primitive variable recover, (3) the treat- ment of stiff source terms characterized by the weak-interaction timescale which is much shorter than the dynamical timescale, which is a troublesome problem due to the relativistic coupling, (4) need for approximate solutions of the Boltzmann equation because of limitation of computational resources, and (5) a problem of the reference frame. We have proposed an approximate method based on the covariant formulation of Moment method by Kip Thorne, to overcome the problems listed above. In this talk, I will give a brief summary of the method. Preliminary results of its applications such as the collapse of a massive stellar core, the merger of binary neutron stars, and evolution of black hole-torus system, will also be presented.

79 Neutron-star mergers in scalar-tensor theories of gravity

Barausse E, Palenzuela C, Lehner L, Ponce M

We show that in scalar-tensor theories of gravity predicting the existence of spontaneously scalarized isolated neutron stars, a related phenomenon takes place in the late stages of the evolution of binary systems. As a result, in regions of the parameter space of these theories where constraints from both solar system experiments and binary-pulsar observations are satisfied, we show that neutron-star binaries may present marked differences from General Relativity in both the late- inspiral and merger phases. These strong-field effects are difficult to reproduce in General Relativity, even with an exotic equation of state, and may be relevant for Advanced LIGO/Virgo.

On the solution space of differentially rotating neutron stars in general relativity

Rosinska D, Kowalska I, Villain L, Ansorg M

An understanding of differentially rotating relativistic stars is key to many areas of astrophysics, in particular to the emission of gravitational waves. A newly born, proto-neutron star or a compact remnant of neutron stars binary merger are expected to rotate differentially and to be important sources of gravitational radiation. A highly accurate, multidomain spectral code is used in order to construct sequences of general relativistic, differentially rotating neutron stars in axisymmetry and stationarity. The high level of accuracy and stability of the code enable us to study stars with maximal masses and high rotation profiles. We investigate the solution space corresponding to broad ranges of degree of differential rotation and stellar densities. We find various types of configurations, which were not considered in previous work, mainly due to numerical limitations. The maximum allowed mass for the new types of configurations and moderate degree of differential rotation can be even 2-4 times higher then the maximum mass of non-rotating neutron stars with the same equation of state. Differential rotation can temporarily stabilize a hyper-massive neutron star against gravitational collapse. We summarize our studies on properties of differentially rotating neutron stars.

Differentially rotating strange quark stars

Szkudlarek M , Gondek-Rosinska D, Villain L, Ansorg M

Strange quark stars are considered as a possible alternative to neutron stars as compact objects. A hot compact star (a proto-neutron star or a strange star) born in a supernova explosion or a remnant of neutron stars binary merger are expected to rotate differentially and be important sources of gravitational waves. We present results of the first relativistic calculations of differentially rotating strange quark stars for broad ranges of degree of differential rotation and maximum densities. Using a highly accurate, relativistic code we show that rotation may cause a significant increase of maximum allowed mass of strange stars, much larger than in the case of neutron stars with the same degree of differential rotation. Depending on the maximum allowed mass a massive neutron star (strange star) can be temporarily stabilized by differential rotation or collapse to a black hole.

80 Strange quark star binaries in the late inspiral phase

Wi´sniewiczM , Gondek-Rosi´nska D

Compact binaries containing a neutron star are one of the most important sources of gravitational waves for ground-based interferometric detectors like LIGO/VIRGO. Gravitational wave signal of the late inspiral or merger hase of such binaries could yield important information about the equation of state of neutron stars. We present first calculations of the final phase of inspiral of irrotational strange star binaries for different mass ratio. Two types of equation of state at zero temperature are used - the MIT bag model and the Dey et al. 1998 model of strange quark matter. We study the precoalescence stage within the Isenberg-Wilson-Mathews approximation of General Relativity using a multidomain spectral method. We find that, in contrast to neutron stars, the innermost stable circular orbit (ISCO) is determined always by an orbital instability for strange stars binaries independently on the total mass of a binary system. The gravitational wave frequency at the ISCO, which marks the end of the inspiral phase, is always higher than 1.1kHz for equal masses irrotational strange stars with the total mass- energy of a binary system greater than 2 solar masses. We find that the dependence of the frequency of gravitational waves at the ISCO on the compactness parameter for the equal mass binaries can be described by the simple analytical formulae for broad ranges of masses independently on a strange star model. Comparisons with neutron star binaries are given.

The nonlinear development of the relativistic two-stream instability

Hawke I

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of rela- tivistic multi-species hydrodynamics we show that the onset and initial growth of the instability is very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.

Simulation of shattering in the neutron star crust

Erickson S

Although the neutron star crust contributes only a small fraction to the total mass of the star, it is expected to affect the dynamics of systems where interface or crustal modes are excited, such as during binary neutron star mergers, where excitation of these modes could lead to tidal shattering of the crust. To model such systems, we have developed a general relativistic conservation-law formalism for nonlinear elasticity; this allows us to use high-resolution shock-capturing methods to resolve strong shocks. We plan to use this formalism, along with appropriate methods for treating the solid-fluid and solid-vacuum interfaces at the edges of the crust, to simulate a toy-model evolution of discontinuities such as those that could be caused by tidal shattering and refreezing of the crust. The toy-model simulation will present numerical challenges that must be solved for more realistic simulations: ie. large variations in temporal and spatial scales between deep inside the star and the surface.

81 Neutron star evolutions with nuclear equations of state

Neilsen D, Anderson M, Lehner L, Liebling S, Palenzuela C

Neutron star properties and structure depend on the nuclear equation of state, which is not well known at high densities. Observations of neutron star mergers with gravitational waves may provide important information about the stellar structure, giving important information about the equation of state. More- over, possible electromagnetic or neutrino emissions from merger events also depend sensitively on the equation of state through fluid temperatures and densities. We explore some effects of nuclear equations of state in binary mergers with neutron stars.

Neutron star dynamics

Liebling S

The dynamics of magnetized neutron stars both in binaries and in isolation are modeled within a fully relativistic, MHD code. The extreme environment of neutron stars, in particular their strong gravity, high density, large magnetic field, and high temperature, allows for significant emissions in both electro- magnetic and gravitational wave bands. The effects of a neutrino cooling via a leakage scheme are also studied.

Bar-mode instability in relativistic rotating stars

Franci L, De Pietri R, Dionysopoulou K, Rezzolla L

We present results on the dynamics and the onset of the classical bar-mode (m=2) instability of differ- entially rotating relativistic star models in presence of non zero magnetic fields. The study is carried out performing full 3D ideal magneto-hydrodynamics simulations, in full General Relativity, superimposing to initial (matter) equilibrium configurations purely poloidal magnetic fields of different strength (in the range 1013-1016 Gauss). For all models we observe a sudden formation, and linear growth, of a toroidal magnetic field component that rapidly overcomes the original poloidal one as a consequence of the winding of the magnetic field lines dragged by differential rotation, and hence an amplification of the total magnetic energy inside the star. Magnetic fields of order 1014 Gauss or less, have negligible effetcs on both stable and unstable models, while greater magnetic fields are able to completely suppress the hydrodinamical instabilities present in the un-magnetized case (the treshold being different for the different unstable models).

New exact solutions to force-free electrodynamics on black hole backgrounds

Gralla S, Brennan D, Jacobson T

Desite four decades of widespread recognition of the importance of force-free electrodynamics in describ- ing compact object magnetospheres, only a handful of exact solutions are known. In the Kerr spacetime, only a single solution (class) has been discovered, the stationary and axisymmetric solution of Menon and Dermer. We analyze the equations from a spacetime perspective (rather than in a 3+1 decompo- sition) and find many new exact solutions. These include non-stationary, non-axisymmetric solutions in Kerr. Our analysis reveals new mathematical and physical properties of the equations of force-free electrodynamics.

82 Merger of binary neutron star: our current status

Shibata M

The coalescence of binary neutron stars and black hole-neutron star binaries is one of the most promising sources of gravitational waves for ground-based laserinterferometric detectors. The merger of these systems is also the promising candidate for short-hard gamma ray bursts and possible source of strong transient electromagnetic emission. The signals of gravitational waves and electromagnetic waves will be detected in the next decade. However for the detection, theoretical predictions are necessary. To strictly predict the properties of these signals, numerical-relativity simulations with the physical modeling are probably the unique approach. In my talk, I will summarize the current status for our numerical-relativity simulations. on binary neutron stars

Generel relativistic simulation of binary neutron star mergers with neutrino cooling

Kiuchi K

Coalescence of binary neutron star merger is one of most promising source of gravitational waves and it is a main target for advance LIGO, advanced VIRGO and KAGRA. To predict waveforms theoretically in merger phase, numerical relativity is a viable approach. We recently developed a numerical code in which a tabulated equation of state and neutrino cooling based on a general relativistic leakage scheme are implemented and explored merger of equal and unequal mass binary neutron stars. We investigated a dynamics and a structure of remnant massive neutron star, such as density, temperature, electron fraction profile and neutrino emission region in details. We compared our models to those studied so far and find that the general relativistic treatment of the gravity and neutrino emission are essential for exploring the binary neutron star mergers. We will talk the results in details.

Eccentric neutron star binaries as revealed by numerical relativity

Johnson-McDaniel N , Bernuzzi S, Br¨ugmannB

We describe the results of our numerical evolutions of highly eccentric neutron star binaries, focusing on the properties of their gravitational waves, accretion disks, and ejecta. In particular, we show the effects of using a realistic equation of state and unequal mass ratios. On the gravitational wave side, we concentrate on the repeated burst structure from the stars’ close encounters and the signal from the tidally induced oscillations of the neutron stars and assess prospects for detection. On the matter side, we consider how the properties of the accretion disk and ejecta from the merger relate to potential electromagnetic signals (e.g., short gamma-ray bursts or radio afterglows) and r-process nucleosynthesis. Finally, we describe our efforts to ensure the accuracy of our simulations.

Core collapse supernovae numerical simulations up to black hole formation to test hot equations of state

Peres B, Oertel M, Novak J

I will present core collapse supernovae numerical simulations up to black hole formation with new equa- tions of state (EoS) containing exotic particles, namely pions and hyperons. I will show results, including

83 differences between a reference (Lattimer and Swesty) EoS and EoS with additional particles (pions, hy- perons). Additional particles are found to soften the EoS so that the black hole collapse happens earlier. The phase transition to hyperonic matter also appears for progenitor stars with large enough accretion rates.

Progress in general-relativistic collapse of massive stars

Reisswig C

We present new results on the fully general-relativistic modeling of stellar collapse to protoneutron stars and the subsequent evolution towards a core-collapse supernova or black hole formation. Our simulations are three dimensional and employ realistic microphysics, including neutrinos and a finite-temperature equation of state. We outline the state of stellar collapse models. We present results using our new multipatch code infrastructure and curvature-based gravitational-wave extraction techniques. While the former improves the accuracy of the extracted waves, the latter is particularly important for capturing the wave signal in simulations of black hole formation.

Simulations of coalescing binary black holes: testing and validation

Scheel M

Gravitational waves from binary black hole systems are expected to be measurable by Advanced LIGO within a few years. The SXS collaboration has constructed a pseudospectral evolution code that can accurately simulate such a system through dozens of orbits, plus merger and ringdown, for generic parameter choices including those that lead to significant precession. We are building a database that so far includes over 100 many-orbit high-accuracy BBH simulations, which can be downloaded and used for LIGO science. We discuss how we estimate errors in these simulations, and we present tests of robustness over different choices of simulation details such as gauge conditions, wave-extraction technique, and initial data formulation.

Binary ns simulations using spec

Haas R, Kaplan J, Szilagyi B, Muhlberger C, Foucart F, Lippuner J, Scheel M, Duez M, Ott C

NSNS binaries are expected to be one of the major sources of gravitational radiation detectable by Advanced LIGO. Together with neutrinos, gravitational waves are our only means to learn about the processes deep within a merging pair of NS, shedding light on the as yet poorly understood, equation of state governing matter at nuclear densities and beyond. We report on binary neutron star simulations using the Spectral Einstein Code (SpEC) developed by the Caltech-Cornell-CITA-WSU collaboration. We simulate the inspiral through many orbits, follow the post-merger evolution, and compute the full gravitational wave signal. We provide estimates on the accuracy required for the LIGO scientific goals of constraining EOS parameters.

Gravitational radiation captures of two black holes in weakly hyperbolic orbits

Kang G, Hansen J, Diener P, Kim H, Loeffler F

We have numerically studied gravitational radiation capturing processes of two non-spinning equal mass black holes in weakly hyperbolic orbits (e.g., eccentricities of 1.0 1.4). Understanding this capturing

84 process is important to evaluate the formation rate of black hole binaries near the supermassive black hole in galactic nuclei. The capturing cross sections obtained in full general relativity agree well with the corresponding 2.5 post Newtonian results for small initial energies, but differ up to about 40% for large initial energies. We also confirmed that most of gravitational wave emissions occur when two black holes encounter closely. This explains why the multipole contributions higher than l=2 are negligible (e.g., about 1%) even if the orbit is quite eccentric or non-quasi-circular. The features of energy and angular momentum extractions and gravitational wave forms are also analyzed.

Calculation of gravitational radiation in characteristic numerical relativity

Bishop N

We re-investigate, within characteristic numerical relativity, formulas for describing gravitational radia- tion at null infinity, and obtain a formula for the gravitational wave strain (h+, h×) that does not require integration of the news or of ψ4. In addition, it is found that a correction needs to be made to the nonlinear terms in the standard formula for the gravitational news. Existing results in the linearized case, and for ψ4, are not affected by the correction.

Primordial black holes and critical collapse within an expanding universe

Musco I

The well-known process of Type II critical collapse has been shown to arise within an expanding universe, in the context of spherically-symmetric simulations of primordial black hole formation. Cosmological perturbations, of the type expected to have come from inflation, have been shown to collapse after horizon crossing and give rise to primordial black holes if the perturbation amplitude is larger than a threshold which depends on the equation of state and the perturbation profile. If the perturbation amplitude is very close to the threshold, the collapse is characterized, over many e-foldings, by an intermediate state, where gravity and pressure balance in such a way as to give a contraction at nearly constant compactness. This intermediate state is a crucial aspect of the critical solution and follows an almost self-similar behaviour. The way in which this matches onto an external expanding FRW solution has been demonstrated. Simulations show also that for perturbations just above the threshold, a relativistic wind blows away matter not trapped by the gravity, forming a deep evacuated region around the forming black hole. Scaling laws have been obtained for the mass and formation-time of the black holes, which have the same exponent whose value depends on the equation of state parameter.

A formalism for weak solutions of gr elasticity

Gundlach C

Motivated by the nonlinear simulation of neutron star quakes, we have extensively tested a formalism for nonlinear GR elasticity that is both symmetric hyperbolic and explicitly in conservation law form. I review the geometrical ideas (due to Carter), typical shock waves, the origin of gauge freedom and constraints, and their role in finding a hyperbolic form of the equations (building on work by Beig and Schmidt).

85 Poster session

Multi-component model of neutron stars with magnetic fields.

Muddle J

Current numerical simulations of magnetised neutron star binary inspiral use different limits of the Einstein-Maxwell-Euler equations. These include Ideal MHD, resistive MHD, force-free and electro- vacuum. An efficient and practical approach evolves each model in the appropriate region, separated by sharp interfaces. We implement this by extending the work of Millmore and Hawke to include magnetic fields. We show our results for SRMHD interfaces where we see vorticity propagation along the field lines, and discuss the interesting dynamical post-merger effects in BNS inspiral.

Numerical simulations on relativistic jets from neutron stars

Lemon T

Significant work has already been carried out on numerical simulations on relativistic jets around compact objects. However most of this work has focused on using black holes as the compact object. Here we consider the effect of a neutron star in an accreting system powering a relativistic jet. The formation process of such jets are still not very well understood, and can be affected by such things as spin and magnetic fields. By studying their formation, it should be possible to find out more about the compact object powering the jet. We describe the numerical methods used to create a general relativistic magneto- hydrodynamical (GR-MHD) model of an accreting system.

General relativistic resistive magnetohydrodynamics: tests and applications

Dionysopoulou K , Alic D, Palenzuela C, Rezzolla L, Giacomazzo B

We present a numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of Implicit- Explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for small electrical conductivities. We show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests involving nonrotating magnetized neutron stars, we report on the collapse of a nonrotating star to a black hole because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electro- magnetic fields. We show that also in this case our results on the quasi-normal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the ` = 1 mode eigenfrequency, respectively. We also provide an estimate of the electromagnetic efficiency of this process. Finally, we show some preliminary results regarding magnetized binary neutron stars.

86 Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

Jasiulek M , Korzynski M

We present a numerical method for solving Weyl’s embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on a construction introduced by Weingarten and was used in Niren- berg’s proof of Weyl’s conjecture. The target embedding results as the endpoint of an embedding flow in R3 beginning at the unit sphere’s embedding. We employ spectral methods to handle functions on the surface and to solve various (non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.

87 B3 - Numerical relativity : methods, theoretical gravity and high energy applications

Oral session

Hyperboloidal evolution of the einstein-yang-mills system

Rinne O, Moncrief V

Hyperboloidal foliations of spacetime, combined with conformal compactification, allow one to include future null infinity in the computational domain, where radiation can be extracted in an unambiguous way. We developed a constrained ADM-like evolution scheme for the Einstein equations on constant mean curvature slices. Recently we have shown how matter can be included in our formulation. Here I will present some new results on numerical evolutions of the Einstein-Yang-Mills system.

Fully spectral code for linear axis-symmetric wave equations on hyperboloidal foliations

P. Macedo R, Ansorg M

We present a new numerical scheme for the time evolution of linear axis- symmetric wave equations around a black hole. The code relies on two features: i) the surfaces of constant time extend all the way towards future null infinity (hyperboloidal slices), which is included in the computational domain by a compactification of the radial coordinate, ii) the wave equations are solved by means of a pseudo-spectral method, which is applied here to both spatial and time directions. The inversion of the resulting dense matrix is efficiently performed with a specifically designed iterative method. We obtain extreme precision of the numerical solution close to machine accuracy, which allows us to study in detail the field’s tail, i.e., the decay as an inverse power law in the asymptotic time evolution.

88 Resonances of massive scalar fields propagating on a black hole spacetime

Barranco J, Bernal A, Degollado J, Diez-Tejedor A, Megevand M, Alcubierre M, Nunez D, Sarbach O

We consider the Klein-Gordon equation on a Schwarzschild background and show the existence of quasi- stationary scalar field configurations whose associated time scale can be extremely large, even larger than the age of the universe, provided the black hole or the scalar field mass is small enough. Scenarios where such long-lived configurations could occur include ultralight scalar field dark matter clouds around su- permassive black holes. We also show numerical and analytic results indicating that these configurations are excited, at late times, in the evolution from fairly arbitrary initial data.

Numerical challenges in the evolution of non-singular ”quantum universes”

Diener P, Gupt B, Singh P

The evolution of the wave-function of a semi-classical universe in isotropic Loop Quantum Cosmology (LQC) is governed by difference equations with uniform discretisation in the spatial direction. We study the numerical simulations of widely spread states, corresponding to ”quantum universes”, which require a large computational domain. These simulations, hence, would be computationally very expensive. In this talk we present an efficient hybrid numerical scheme based on the fact that LQC difference equations can be approximated by partial differential equations (PDE’s) in the large spatial volume domain. We introduce a mixed spatial grid where we solve the LQC difference equations in the small volume regime and the PDE’s in the large volume regime. By a simple coordinate transformation, we obtain a huge reduction in the cost of the computation. This scheme enables us to explore the regions of the parameter space which was previously unachievable. We describe the numerical properties of the scheme and present selected results.

Linearised gravitational fields near space-like and null infinity

Frauendiener J

The conformal compactification introduced by Penrose in the late 1960s provides an interesting approach towards the numerical simulation of global properties of space-times. The work by Friedrich has put Penrose’s approach onto a firm mathematical footing, giving wellposedness and stability results for several finite initial (boundary) value problems of the (generalized) conformal field equations. In this talk we will discuss the geometrical and analytical foundations of these ideas and we present numerical results for the evolution of linearized gravitational fields i.e., the zero-rest-mass spin-2 fields on Minkowski space.

Formation of wormholes in gravitational collapse

Nakonieczna A

Due to apparently common presence of dark energy in the Universe the question of its impact on various astrophysical processes arises. One of the processes which may be influenced by dark energy is gravita- tional collapse. The toy-model for the realistic version of it is the evolution of electrically charged scalar field.

89 One of observationally accepted theoretical models of dark energy is provided by phantom fields. On the other hand, such fields ensure stability of wormhole throats in non-dynamical cases. The aim of our studies was to investigate the possibility of formation of such objects during gravitational collapse. It turned out that spacetimes emerging from the evolution of electrically charged scalar field in the presence of phantom dilaton field contain dynamical wormholes. We concentrated on the structure of spacetime and properties of matter in the vicinity of wormhole throats. Apart from describing spacetime structures we investigated the properties of wormholes formed during the considered process. We inspected the dependence of their characteristics on initial amplitudes of evolving fields. Moreover, the performed analyses provided an example of duality between black holes and wormholes in the dynamical case.

Quantum quenches in strongly coupled systems from ads/cft correspondence

Buchel A, Lehner L, Myers R, van Niekerk A

We exploit gauge theory/string theory correspondence to study quantum quenches in strongly coupled gauge theory plasma. Specifically, we consider the response of a thermal equilibrium state of the theory under variations of the coupling of a relevant operator. We discuss the transition from the ’adiabatic’ regime (quenches slow on a thermal time-scale) to ’abrupt’ changes (quenches fast on a thermal time- scale). We comment on relaxation mechanisms and rates for non-equilibrium states produced by a quench. We emphasize the ambiguities in definition of gauge-invariant operators in the theory off the equilibrium, and propose the renormalization scheme-independent definition of some of these operators. All the computations are performed in a dual holographic frame represented by scalar-Einstein gravity in asymptotically AdS space-time. We study numerically the dynamics of a scalar field in a planar AdS- black hole geometry, and use holographic dictionary to map the results of the simulations to Quantum Field Theory frame.

Numerical methods for stationary non-killing horizons and applications to holography

Figueras P

In this talk I will present a new method to numerically construct stationary black hole spacetimes which have a non-Killing horizon. As I shall explain, the computational domain comprises the domain of outer communications of the black hole as well as a portion of its interior, which naturally leads to a mixed elliptic-hyperbolic problem. As a concrete example, I shall discuss how one can use AdS/CFT to construct the gravitational dual of a time-independent CFT plasma flowing through a static spacetime which asymptotes to Minkowski in the flow’s past and future, with a varying spatial geometry in-between. When the boundary geometry varies slowly, the holographic stress tensor is well-described by viscous hydrodynamics. For fast variations it is not, and the solutions are stationary analogs of dynamical quenches, with the plasma being suddenly driven out of equilibrium. For sufficiently strong quenches these flows become unstable and speculate that the instability may be turbulent. The gravitational dual of these flows are the first examples of stationary black holes with non-Killing horizons. This work was done in collaboration with T. Wiseman and appeared in arXiv:1212.4498.

Black funnels and black droplets: heat transport in strongly coupled cfts from holography

Fischetti S, Marolf D, Santos J

We construct the bulk duals to strongly coupled conformal field theories on black hole backgrounds

90 in the context of the AdS/CFT correspondence. We argue that there are two possible bulk solutions, corresponding to confined- and deconfined-like phases of in the CFT. The deconfined phase of the CFT, characterized by an exchange of heat between the black hole and infinity, is dual to so-called black funnels. In the confined phase, the CFT forms a plasma around the black hole, and heat transport out to infinity is suppressed; we dub the corresponding bulk solution a black droplet. We discuss analytical and numerical construction of black droplets and black funnels in various dimensions and compare our numerical results to analytic ones obtained from the fluid/gravity correspondence. In a regime where the local CFT temperature is much greater than that of the boundary black holes, our numerical results are in excellent agreement with the fluid/gravity expectation.

Time-periodic solutions in einstein ads — massless scalar field system

Maliborski M

I will present recent results (joint work with Andrzej Rostworowski) concerning a system of self-gravitating massless scalar field, with negative cosmological constant, in d+1 spacetime dimensions at spherical sym- metry. I will focus on time-periodic solutions for this system — perturbative and numerical construction procedure. To confirm our results I will show the outcomes of direct numerical integration which gives a strong evidence for nonlinear stability of these special solutions. To show the consistency of the results I will comment on the convergence radius of the formally obtained perturbative series, the convergence domain of our numerical method and the threshold for the black-hole formation. In the summary I will remark about possible generalization to other models.

Stability of test fields propagating on a collapsing spherical dust cloud.

Ortiz N , Sarbach O

We consider the Cauchy horizon stability of a globally naked singularity resulting from the spherical collapse of a dust cloud. To gain some insight into this problem we analyze the propagation of scalar and electromagnetic test fields on a collapsing dust background. First, we study the high frequency limit and show that the blueshift of in- and outgoing null rays is uniformly bounded near the singularity. Next, we implement a characteristic numerical algorithm to analyze the propagation of the test fields near the Cauchy horizon. The simulations indicate that, while the scalar field is bounded, its gradient diverges at the Cauchy horizon. We also perform energy estimates showing analytically the L2-boundedness of the scalar field’s gradients and of the electromagnetic field.

The black-hole bomb mechanism in astrophysical environments - part 1

Okawa H , Witek H, Cardoso V

Black holes are key players in fundamental physics including astrophysics as well as high energy physics. Crucial questions concern their stability properties with potentially important implications for the phase- space of solutions or the understanding of condensates in the vicinity of black holes. Of particular interest is the superradiant or ”BH-bomb” like instability of Kerr BHs which arises naturally in the presence of massive fields surrounding the BH. While the (in-)stability of BHs against massive scalar fields is well understood on the linear level, we have explored their interaction in the fully non-linear regime of GR. The presence of a scalar condensate in the vicinity of the BH gives rise to long-lived, almost constant frequency gravitational wave emission and might even have the potential to trigger GW wave pulsars.

91 Here, we wish to show how we describe such a system with the BH in the method of Numerical Relativity.

The black-hole bomb mechanism in astrophysical environments - part 2

Witek H

Black holes are key players in fundamental physics including astrophysics as well as high energy physics. Crucial questions concern their stability properties with potentially important implications for the phase- space of solutions or the understanding of condensates in the vicinity of black holes. Of particular interest is the superradiant or ”BH-bomb” like instability of Kerr BHs. which arises naturally in the presence of massive fields surrounding the BH. While the (in-)stability of BHs against massive scalar fields is well understood on the linear level, we have explored their interaction in the fully non-linear regime of GR. The presence of a scalar condensate in the vicinity of the BH gives rise to long-lived, almost constant frequency gravitational wave emission and might even have the potential to trigger GW wave pulsars. Here, we wish to present our numerical results of long-time evolutions of massive scalar fields in. generic BH environments.

Reduced-order modeling of binary black hole coalescences

Galley C

Reduced Basis is a reduced-order modeling technique for parameterized problems, such as the solutions of ordinary or partial differential equations. The advantage is that once the reduced model is con- structed one can efficiently and rapidly generate accurate approximations of the full solution for any given parameter value. Solving Einstein’s equations for the coalescence of binary black holes takes a substantial amount of time (often months) and computational resources to generate a single solution. A reduced-order model would provide a way to generate, in the matter of seconds or faster, an accurate approximation of a gravitational waveform for any given parameter value, which can then be used in place of running expensive simulations. In this talk, I discuss how a reduced-order model based on the recently developed Reduced Basis Method can be used to estimate which binaries are the most relevant ones to simulate for building the reduced model. Results are presented for non-spinning binary black hole coalescences.

Black hole spin within the moving puncture method: numerical experiments

Dietrich T , Br´ugmannB

The moving puncture method is an important tool in numerical relativity since it allows long term simulations of black holes. An essential component of the moving puncture method is the use of the 1+log slicing condition. We reproduce known results of 1+log-slices of the Schwarzschild spacetime and enlarge the parameter space by considering also rotating black holes. The results of the stationary Schwarzschild 1+log-trumpet have to be modified when we add spin. The influence on the BSSNOK- variables leads to a simple and cheap algorithm for determining the spin of a non-moving black hole. We check the results of the new method with the help of single black hole, binary neutron star and mixed binary simulations.

92 Iterative stability of the einstein constraint equations

Markakis C , Price R, Br¨ugmannB, Friedman J

When solving the Einstein constraints with the self-consistent field method in the extended conformal thin-sandwich (XCTS) approach, the iteration may diverge for highly compact sources, or may converge to an unphysical solution. The basis of these inconsistent convergence properties is not well understood. We study the behavior of this iterative scheme near an exact static solution, treating one cycle of iteration as an updating operator. We obtain the spectrum of the linearized iteration operator and show that iterative instability is associated with unstable modes of this operator that appear at high compactness. We reformulate the XCTS system so as to minimize the maximum eigenvalue of the updating operator, rendering the iteration unconditionally stable. This optimization accelerates convergence and allows computation of highly compact configurations that were previously inaccessible via self-consistent field methods.

Axion bosenova and gravitational waves

Yoshino H , Kodama H

It was pointed out that string theory predicts the existence of 10-100 axionlike fields with ultralight mass. These string axions may cause observable phenomena in cosmology and astrophysics, opening up a possibility of detecting evidences for string theory through observations. If an axion has the Compton wavelength comparable to the radius of an astrophysical black hole (BH), the axion field forms a cloud extracting the BH rotation energy. One of the expected phenomena of the BH-axion system is the ”bosenova” caused by axion’s nonlinear self-interaction, which is analogous to explosions observed in experiments of Bose-Einstein condensate. We perform simulations of axion field in a Kerr spacetime and show that the bosenova actually happens. Also, we would like to introduce our ongoing studies on gravitational waves emitted in the bosenova and point out the possibility of their detection in future observations.

93 Poster session

Time evolution of non-symmetric robinson-trautman spacetimes

Macedo R, Saa A

We consider the time evolution of nonsymmetric Robinson-Trautman spacetimes. We employ a Galerkin approximation and show that regular initial data evolve generically into a final configuration correspond- ing to a Schwarzschild black-hole moving with constant speed. The relation with the gravitational wave recoil is discussed. This work is a natural extension of [1]. [1] R.P. Macedo and A. Saa, Phys. Rev. D 78, 104025 (2008)

Wormhole evolutions in higher-dimensional gravity – effects of gauss-bonnet gravity terms

Shinkai H , Torii T

We know numerically the four-dimensional Ellis wormhole solution (the so-called Morris-Thorne’s traversible wormhole) is unstable against an input of scalar-pulse from one side [1]. We investigate this feature for higher-dimensional versions, both in N-dimensional general relativity and in 5-dimensional Gauss-Bonnet gravity [2]. We derived Ellis wormhole solutions in N-dimensional general relativity, and predicted their instability using perturbation method. We, then, evolved the 5-dimensional solution numerically in dual-null co- ordinate with/without Gauss-Bonnet corrections. Numerical evolutions confirm wormholes’ instability. We also find that the throat of wormhole in Gauss-Bonnet gravity tends to expand (or shrink) after an input of ghost-scalar pulse if the coupling constant is positive (negative). [1] H. Shinkai & S.A. Hayward, Phys. Rev. D66, 044005 (2002) [2] T. Torii & H. Shinkai, in preparation

Radiation from a d-dimensional collision of shock waves

Coelho F, Herdeiro C , Rebelo C, Sampaio M

I will describe our group’s work on ”Shock wave collisions” as a semi-analytical technique to understand the collision of two black holes, head-on, at very high speeds in D space-time dimensions. The geometry describing the future of the collision of two Aichelburg-Sexl shock waves can be computed using a perturbative framework, first discussed in four space-time dimensions by D’Eath and Payne. We reanalyse and extend this framework to obtain the radiated energy in gravitational waves, i.e. the inelasticity, in D dimensions. In particular we present a remarkable pattern for the inelasticity in terms of the space-time dimension, obtained in first order perturbation theory. Comments will be made about the applicability of perturbation theory, higher order corrections and comparisons with collisions of black holes and other compact objects using numerical relativity simula- tions.

94 Well-posedness of characteristic evolution in bondi coordinates

Babiuc M

Gravitational waves carry information about their source, and their detection will uncover facets of our universe, otherwise invisible. Recently, we made publicly available a waveform computation tool, the PITT code, as part of the Einstein Toolkit open software for relativistic astrophysics. The code imple- ments the characteristic method, which computes the gravitational waves infinitely far from their source in terms of compactified light cones. We proved that our code produces waveforms that satisfy the demands of next generation detectors. However, the main problem is that the well-posedness of the Ein- stein equations in characteristic formulation is not proven. I will present our progress towards developing and testing a new computational evolution algorithm based on the well-posedness of the characteristic evolution. We analyze the well-posedness of the problem for quasilinear scalar waves propagating on an asymptotically flat curved space background with source, in null Bondi-Sachs coordinates. We design a new numerical boundary and evolution algorithm, and proved that is stable both numerically and analytically. We built and run numerical tests to confirm the well-posedness and stability properties of the new algorithm. Next step is to extend this treatment to the simulation of gravitational waves in the full nonlinear context of general relativity. A new characteristic code based upon well-posedness would be of great value.

Initial data for eccentric neutron star binaries

Moldenhauer N , Markakis C, Br¨ugmannB

We present a way to construct initial data for neutron star binaries on quasi-circular or eccentric orbits. Therefore a self-consistent field method is used, which solves the Einstein constraints in the conformal thin-sandwich approach. A single TOV star can be constructed in this way and afterwards, two such TOV stars are superimposed. Then the method is applied again to minimize the constraint violations and induce tidal deformations.

Numerical solution of the 2+1 teukolsky equation on a hyperboloidal and horizon penetrating foliation of kerr

Harms E, Bernuzzi S, Bruegmann B

We present a novel formulation of the Teukolsky equation for generic spin perturbations on the hyper- boloidal and horizon penetrating fo- liation of Kerr proposed recently by Racz and Toth. An additional, spin-dependent rescaling of the field variable can be used to achieve stable, long-term, and accurate time- domain evolutions of generic spin perturbations. As an application we investigate numerically the late- time decays of scalar, electromagnetic, and gravitational perturbations by means of 2+1 evolutions.

95 Spherical symmetry as a test case for unconstrained hyperboloidal evolution

Vano-Vinuales A, Husa S

We consider the problem of utilizing the hyperboloidal initial value problem for an efficient numerical construction of spacetimes which could be used to evolve radiating compact objects such as black hole binaries. Unconstrained evolution schemes could allow for optimal efficiency, but are difficult to regular- ize. Spherical symmetry already poses nontrivial problems and constitutes an important first step. We find a beneficial class of evolution equations for the lapse function, and regularize and numerically evolve various hyperbolic subsystems of the BSSN and Z4 equations.

96 B4 - Analytic approximations, perturbation theory, effective field theory methods and their applications

Oral session

Perturbations of slowly rotating black holes: framework and applications.

Pani P

We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. The framework can be applied to a variety of situations. In the slow-rotation limit, we study (i) superradiant instabilities of Kerr black holes against massive spin-0, spin-1 and spin-2 fields; (ii) the quasinormal- mode spectrum of Kerr-Newman black holes. Extensions to nonKerr solutions in modified gravity and to higher-dimensional spinning black holes are discussed.

Probing dynamical chern-simons gravity with gravitational-wave and pulsar observations

Yagi K , Stein L, Yunes N, Tanaka T

The study of how well one can test General Relativity in the strong, non-linear and dynamical regime is essential. As an example, we focus on tests of dynamical Chern-Simons gravity, which is the only parity-violating, quadratic-curvature theory with a single dynamical axion, and is well-motivated by several fundamental theories, such as heterotic superstring theory. With the new, quadratic-in-spin black hole solutions we recently found, we construct a self-consistent gravitational waveform from black hole binaries in the inspiral phase. We find that both dissipative and conservative corrections enter at 2nd post-Newtonian order in the waveform and couple to spin. The network of second-generation ground- based interferometers will be able to place constraints that will be 6 orders of magnitude stronger than current Solar System ones. Next, we construct slowly-rotating neutron star solutions and calculate corrections to the neutron-star mass and the post-Keplerian parameters in a binary system. We find that it would be difficult to obtain any meaningful constraint from pulsar observations, which implies that gravitational wave observations might be the only ways to constrain this theory strongly.

97 Eccentric binary effects in dynamical chern-simons gravity

Stein L, Yagi K, Yunes N, Tanaka T

One of the most promising natural laboratories for testing corrections to general relativity is an eccentric pulsar binary such as J0737-3039. The correction on which we focus is dynamical Chern-Simons (DCS) gravity, a theory containing a parity-odd scalar, motivated by fundamental physics. Because of parity violation, DCS exhibits corrections distinct from well-studied even-parity theories (Brans-Dicke). We compute the leading conservative and dissipative corrections to the orbit, most importantly the rate of pericenter advance, change in inclination, and the ascending node, and less prominent effects such as the correction to the orbital decay and the precession of the bodies’ spins. Given how (non-)relativistic the presently-known systems are, we comment on the difficulty of constraining DCS with presently available data.

Gravitational perturbations of higher dimensional rotating black holes in ads and cosmic censorship

Rocha J

Cosmic censorship is a cornerstone of general relativity, essentially postulating self-consistency of the theory. Recent developments raised justified concerns about the validity of the conjecture for higher- dimensional gravity but relatively little is known regarding cosmic censorship in non-asymptotically flat spacetimes. A stringent test of the conjecture consists in throwing point particles with sufficiently large angular momentum into an extremal or near-extremal rotating black hole and determining if the black hole is overspun. This has been considered in the past for asymptotically flat spacetimes and we will extend this program to anti-de Sitter (AdS) black holes. In particular, we study linearized gravitational perturbations induced by test particles on odd dimensional Myers-Perry black holes with all angular momenta equal. Although these backgrounds are rotating they are known to be cohomogeneity- 1 solutions, which allows for an analytic treatment. By solving the perturbation equations we identify the energy and angular momenta of point particles in AdS and test the cosmic censorship conjecture in non-asymptotically flat spacetimes.

Conformal symmetry and the gregory-laflamme instability

Camps J

Higher dimensional Ricci-flat black branes suffer from the Greogry-Laflamme instability. In this talk I will present a very simple and efficient long-wavelength approximation to this instability. This hydrodynamic approximation exhibits a conformal symmetry much like in AdS/CFT, where gravitational modes in AdS encode CFT quantities. This fact links to recent developements suggesting that conformal symmetry plays a role in all kinds of black holes, including Ricci-flat ones.

The structure of the retarded green function in schwarzschild spacetime from large ` asymptotics.

Nolan B, Casals M

The fourfold singularity of the Green function for wave equations in curved spacetimes with caustics has been discussed on several occasions in the recent literature (Ori, Casals et al, Drivas & Harte, Casals

98 & Nolan, Dolan & Ottewill), in the context of the self-force problem. We provide further detail on this fourfold structure for waves on Schwarzschild black holes by application of large ` asymptotic anaylsis of the 1+1 dimensional Regge-Wheeler equation and resummation of the asymptotic solution for the `-modes. This allows us to relate the leading order coefficients of the global singular structure of the Green function to coefficients of the local singular structure (i.e., the Hadamard form).

Isofrequency pairing of geodesic orbits in kerr geometry

Warburton N , Barack L, Sago N

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to- one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain ”synchronized” in phase.

Estimates for the effects of transient resonances in extreme mass ratio inspirals

Hinderer T , Flanagan E

Future observations of inspirals of compact objects into much more massive black holes could provide unprecedented tests of General Relativity and high precision measurements of the system parameters. Detecting the gravitational waves from these signals and extracting the science payoffs from the data is contingent on sufficiently accurate theoretical models. For special classes of orbits, the inspiral can be approximated as an adiabatic flow through a sequence of geodesics. Generic orbits, however, will pass through orbital resonances that occur when the ratio of the radial and polar frequencies, which is slowly evolving under gravitational radiation reaction, is a low order rational number. If the central object is different from a black hole, the low order resonances could indicate regions in the phase space where orbits are most likely to become chaotic. The effect of resonances on the inspiral dynamics when compared to a resonance-free evolution are sudden jumps in the constants of motion that are sensitive to the initial conditions. The jumps effect the frequencies and for transient resonances lead to phase errors that scale as the square-root of the inverse of the mass ratio. Estimates for net size of the kicks and phase errors can be obtained for a wide range of parameters by using analytical approximation methods together with post-Newtonian radiation-reaction forces.

The importance of resonances for the evolution of extreme-mass-ratio inspirals

Cole R, Berry C, Canizares P, Gair J

Extreme-mass-ratio inspirals are some of the most promising gravitational wave sources for a space- based detector. A compact object orbits in the spacetime of a much more massive companion, slowly inspiralling as it loses energy and angular momentum. Such an inspiral may last for 105 cycles, allowing a detailed map of the spacetime to be inferred from the waveform. To extract the waveform from the

99 data, and to correctly perform parameter estimation, we must have accurate waveform templates; even small errors can lead to significant dephasings after 105 cycles. We consider the effects of passing through an orbital resonance when the radial and polar frequencies are rational multiples of each other. While a generic non-resonant orbit ergodically fills a volume of space, resonant orbits trace out a one-dimensional path. Terms in the self-force that usually average to zero can then combine coherently, producing an enhanced or reduced flux of energy and angular momentum, depending upon the relative phase of the radial and polar motions. Intuitively, we expect the effect to be greater for low order resonances, when the frequencies are related by a ratio of small integers; higher order resonances come close to many points and so appear more like non-resonant orbits. We present preliminary results characterising the location and relative importance of resonances and develop a simple model for the transition through a resonance that accounts for the appropriate changes in fluxes.

Regularisation of the detweiler-whiting singular field in kerr spacetime

Heffernan A

Previously, we computed expressions for the Detweiler-Whiting singular field of point scalar, electromag- netic and gravitational charges following a geodesic of the Schwarzschild spacetime. We now extend this to the case of equatorial orbits in Kerr spacetime, using coordinate and covariant approaches to compute expansions of the singular field in scalar, electromagnetic and gravitational cases. As an application, we give the calculation of previously unknown mode-sum regularisation parameters. We also propose a new application of high order approximations to the singular field, showing how they may be used to compute m-mode regularization parameters for use in the m-mode effective source approach to self- force calculations. We give examples of this new scheme in both scalar and gravitational cases in Kerr spacetime.

Properties of the particle model in the null gauge

Moreschi O, Gallo E

There are several ways in which one can approach the notion of compact object in general relativity; for example: * From the notion of isolated systems; through the study of asymptotically flat spacetimes. * Through the study of local solutions to distributions with support on a timelike world line. The previous situation motivates the study of extending the particle paradigm to the relativistic regime, in which the gravitational radiation effects are taken into account in the calculation of the equations of motion. In a previous work we have studied the notion of a particle where the seeds were solutions of linearized gravity calculated from retarded Green’s functions of the first order equations in the harmonic gauge. We here present an approach to the particle paradigm, where no restriction on the weakness of the sources are imposed, nor slow motion is assumed. In particular we present a workable model for the binary system in general relativity. The construction is based on the null gauge and is expected to provide with better results for the regime where back reaction to the motion, due to the emission of gravitational radiation, is important.

Worldline deviations

Saravanan S, D’Ambrosi G, van Holten J

In general relativity, only relative acceleration has an observer-independent meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We

100 derive the world-line deviation equations up to second order, in the conventional geometric formalism. This allows us to generalize the results to test bodies with charge and /or spin. Further, I will state the applications of the equations to the motion of particles in a central field. This may result, in contrast to Post-Newtonian method, a fully relativistic way of describing the dynamics of extreme mass-ratio systems.

Extreme mass-ratio inspiral in a radiation gauge

Shah A, Le Tiec A, Whiting B, Friedman J

We review work on computing the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. A Hertz potential is used to construct the metric perturbation from the perturbed Weyl scalar in a radiation gauge. The reconstruction is complete up to changes in in mass, angular momentum and center of mass, and these are added in an arbitrary gauge. For particles in circular orbit, the perturbed redshift factor, written as a function of angular velocity, is invariant under gauge transformations generated by helically symmetric vectors, and we obtain agreement to numerical accuracy with Lorenz-gauge and post-Newtonian computations. This quantity can also be used to obtain conservative, post-Newtonian parameters at orders that are not currently analytically accessible. We report the current status of a computation with apparent accuracy exceeding 300 digits.

On the 4th post-newtonian hamiltonian dynamics of compact binary systems

Jaranowski P, Schaefer G

We will present recent results concerning derivation of the conservative equations of motion of compact binary systems up to the 4th post-Newtonian approximation of general relativity. The derivation is made within the ADM canonical formalism. It employs Dirac delta distributions to model the compact bodies what leads to divergencies which are regularized by a combination of Riesz-implemented Hadamard’s partie finie approach and dimensional regularization.

Binary system gravitational dynamics at fourth post-newtonian order

Sturani R, Foffa S

We report on the status of our ongoing work about the conservative dynamics of a gravitationally bound two-body system at 4th post-Newtonian order within the effective field theory framework. The computation involves the analysis of over five hundred Feynman diagrams via an algorithm implemented in Mathematica, generating hundreds of terms in the effective two-body Lagrangean. We have checked for Lorentz invariance as it is a power tool to constrain the yet un-computed terms in the effective Lagrangean. The final result includes terms proportional to Newton’s constant to the fifth power which are Lorentz invariant on their own, at this PN order. Their derivation involve 4-loop, 2-external particle Feynman integrals in 3 euclidean dimensions, not previously known in literature. The computation of the 4PN dynamics has a direct application into template construction for gravitational wave detection.

101 Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems

Bohe A

In this talk, we present our computation of the next-to-next-to-leading order spin-orbit contributions to the equations of motion and of spin evolution for binaries of compact objects. The calculation is based on a description of the system using the pole-dipole formalism for point particles and on a post- Newtonian iteration of the field equations in harmonic coordinates. For maximally spinning black holes, those contributions are of 3.5PN order, improving our knowledge of the equations of motion, already known for non-spinning objects up to this order. Checks of the results include: (1) the existence of a set of conserved integrals of the motion; (2) the approximate manifest global Lorentz invariance of the equations of motion in harmonic coordinates; (3) the recovery of the motion of a spinning particle on a Kerr background in the test-mass limit; (4) the existence of a contact transformation, together with a redefinition of the spin variables, that makes our result equivalent to a previously published result obtained from the Arnowitt-Deser-Misner (ADM) Hamiltonian formalism.

Gravitational wave spin-orbit flux and phasing of spinning compact binaries at the next-to-next-to-leading order

Marsat S

We present our computations of the next-to-next-to-leading order spin-orbit contributions to the energy flux emitted in gravitational waves by compact binary systems, corresponding to the 3.5PN order for maximally spinning objects. Following our recent derivation of the corresponding spin-orbit 3.5PN contributions in the equations of motion, we compute the source multipole moments of the compact binary within the multipolar post-Newtonian wave generation formalism. Our results are valid for general orbits and in an arbitrary frame, and are then specialized to quasi-circular orbits. We check the test-mass limit of the final result by recovering the already known Kerr black hole perturbation limit. Furthermore we are able to check that the quadrupole moment of the compact binary reduces in the one-body case to that of a single boosted Kerr black hole. We discuss the implications of our new result in terms of the binary’s phase evolution, and address its importance for the future detection and parameter estimation of gravitational wave signals.

Measurement of spin for inspiralling gravitational wave binaries

Nielsen A

Ground based gravitational wave detectors are sensitive to the inspiral, merger and ringdown of binary systems of stellar mass compact objects. Measuring the mass of these systems is important for classifying them as either neutron stars or black holes, but also the spin of these objects affects the signal that will be measured by the detector. The effect of spin on the signal is however often degenerate with the effect of mass and in particular the individual spins of two bodies are strongly degenerate with each other in the signals they produce. This makes it difficult to determine the individual spins of the inspiralling bodies for all but exceptional cases. We discuss this in the context of up-to-date post-Newtonian waveforms for spinning inspiralling systems.

102 Efficient gravitational wave phasing for spinning compact binaries

Gupta A, Gopakumar A

We develop a prescription to perform gravitational wave (GW) phasing for spinning compact binaries inspiraling along quasi-circular orbits while using the orbital angular momentum rather than its New- tonian counterpart. In our approach, temporally evolving GW polarization states are specified by nine independent parameters, compared to eleven in the traditional approach, as we freely specify the spin vectors in an invariant frame associated with the initial direction of total angular momentum and list the salient features. The above reduction in independent parameters is impossible to achieve in the traditional approach that freely specify the spin vectors in an orbital triad initially. We list a number of undesirable consequences of the traditional approach including the existence of unphysical 3PN order terms in the GW phase evolution.

Gravitational-wave tails-of-tails at the third and a half post-newtonian order

Faye G

In view of providing improved templates for processing and analysing the data that will be soon collected by the advanced ground-based interferometers Virgo and LIGO, we carry on our program to compute the amplitude of the waveform generated by inspiralling compact binaries at the third and a half post- Newtonian order. At such a high accuracy level, among other nonlinear effects affecting the wave propagation, we notably calculate the tails-of-tails interactions between two monopoles and either the mass octupole or the current quadrupole of the system. Physically, those represent the scattering onto the spacetime curvature of tails of waves, which are themselves produced by the curvature scattering of the corresponding multipolar pieces of the linear waves.

Tidal interactions of compact binaries

Steinhoff J , Chakrabarti S, Delsate T

Tidal interactions are of great importance for the inspiral and merger of binaries involving neutron stars. Effective point-particle actions for the binary’s constituents allow a treatment of these interactions within approximations schemes, such as the post-Newtonian approximation. Analytic effective one-body models implementing tidal interactions can provide accurate gravitational wave forms for binary neutron stars. In the present talk we discuss how resonances of the neutron star’s oscillation modes with the tidal field/orbital motion can be incorporated in this framework. These resonances were treated in great detail in the Newtonian limit. There tidal interactions can be described using an amplitude formulation for perturbations of the star and overlap integrals giving the external force. We reformulate this Newtonian framework in a novel way using an effective action. We argue that this reformulation can be generalized to the general relativistic case. We outline our plan to achieve this generalization. However, we also discuss several subtle problem that must be addressed.

Gravitational wave observables from spinning compact binaries with effective field theory

Ross A

This talk will report on some recent progress using the effective field theory framework NRGR. In

103 particular, I will present the current status of the calculation of the phase to 3PN including all spin effects.

Gravitational self-force in the ultra-relativistic limit

Galley C

Using the effective field theory formalism, I discuss the gravitational self-force on a small compact ob- ject in the ultra-relativistic limit where the boost factor γ becomes arbitrarily large. Drawing parallels with the large N limit in quantum field theory, a parameter N = γ2 is introduced and used to show how the effective action admits a well defined expansion in the ultra-relativistic limit. In this limit, many simplifications arise allowing one to compute self-force effects to high orders in perturbation the- ory. In particular, diagrams with nonlinear bulk interactions are subleading so that only diagrams with nonlinearities in the worldline couplings, which are significantly easier to compute, survive in the large N/ultra-relativistic limit. Results are presented for the self-force through fourth order and then special- ized to circular orbits in a Schwarzschild background. Finally, I discuss some aspects of the problem of finding the self-force in the exact massless limit for a photon moving in a black hole spacetime.

Post-linear perturbations in presence of extra dimensions and transplanckian bremsstrahlung

Galtsov D, Spirin P

Post-linear formalism (PLF) of General Relativity is extended to models with toroidal extra dimensions and used to calculate gravitational bremsstrahlung in transplanckian collisions in ADD model of TeV- scale gravity. The theory can be interpreted as emission of massless multidimensional gravitons or, alternatively, as emission of massive modes in four dimensions. The total radiation loss at the fixed impact parameter increases as certain power of the Lorentz factor of the collision which depending on the number of toroidal extra dimensions. We discuss various PLF applicability restrictions on the impact parameter and consider the high energy limit on the boundary of applicability window. Ignoring quantum restrictions, we obtain that the particle energy is fully depleted in colisions with the impact parameter much larger than the gravitational radius of the (presumably) created black hole for large enough number of extra dimensions. The multidimensional PLF is compared and contrasted to D’Eath- Payne type approach to the same problem.

A theory of post-newtonian radiation and self-force

Kol B, Birnholtz O, Hadar S

The talk will describe an effective field theory for the post-Newtonian radiation and self force of a binary system with several novel ingredients. Non-relativistic gravitational fields and non-quantum Feynman rules will be incorporated as well.

104 B5 - Observational cosmology

Oral session

The bright and dark side of cosmic voids - how to measure dark matter distribution in cosmic voids

Bolejko K

More than half of the volume of our Universe is occupied by cosmic voids. Cosmic voids are regions where matter density is much below the mean density of the Universe. In galaxy surveys they appear as vast empty spaces between filaments, which contain very few or no galaxies. Cosmic voids are not merely regions of galaxy avoidance they also affect optical properties of the Universe. During the talk I will discuss how imagines of background objects are distorted when observed through cosmic voids. I will show how these distortions can help us to understand various phenomena and how we can use them to measure dark matter distribution in cosmic voids

The mean transmission in the ly-alpha forest within 2¡z¡4

Ivashchenko G, Torbaniuk O

The large ground-based redshift surveys of quasars allow to study the chemical and thermal evolution of the Universe, as far as the distribution of matter on intergalactic scales via the Ly-alpha forest over the redshift range 2-6. The medium spectral resolution of these surveys does not allow to fit the continuum level within the Ly-alpha forest manually as in high-resolution spectra, but having the large number of spectra they allow more accurate determination of the evolution of the mean transmission ¡F¿ in Ly- alpha forest. We present our measurements of redshift dependence of the mean transmission ¡F(z)¿ of the neutral intergalactic medium in the Ly-alpha line. For this purpose the sample of 3285 medium-resolution spectra from the Sloan Digital Survey Data Release 7 was used. Our own technique of continuum fitting was developed and used for this purpose. It is based on the similarity of quasar spectra and involves the use of composite spectra stacked from the quasar spectra with similar spectral index. The obtained ¡F(z)¿ dependence are well consistent with the results of previous studies of high- and medium-resolution spectra.

105 Inference of the cosmological parameters from gravitational waves observations

Del Pozzo W , Li T, Messenger C

With the advent of the advanced world-wide network of gravitational waves (GW) observatories and in view of the proposed third generation Einstein Telescope observation, we are on the verge of a new era in observational cosmology. GWs from coalescing binaries allow a direct measurement of the luminosity distance without the need of a cosmic distance ladder. Unfortunately, GW, in general, do not yield information about the redshift of a source, which must be obtained by other means. However, when the merger involves neutron stars, by modeling their tidal deformability an estimate of the redshift can be obtained directly from GW. Using simulated data from Einstein Telescope, I will demonstrate that an independent test of the current cosmological paradigm is possible and that the accuracy with which the cosmological parameters can be measured is competitive with traditional electro-magnetic methods.

Why multi-tracer surveys beat cosmic variance

Leonard K , Abramo L

Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement derives from comparing the relative clustering between different tracers of large-scale structure. We present a simple Fisher information matrix for surveys with any number of tracers, and show that the enhancement of the constraints on bias-sensitive parameters are a straightfor- ward consequence of the multi-tracer Fisher matrix. The diagonalized multi-tracer Fisher matrix clearly shows that while the effective volume is bounded by the physical volume of the survey, the relational information between species is unbounded. In our toy model we find enhancements as large as a factor of 3 for the accuracy in the determination of the redshift distortion parameter, and a factor of 5 for the local non-Gaussianity parameter.

106 Poster session

First cosmological constraints on the superfluid chaplygin gas model

Lazkoz R, Montiel A, Salzano V

In this work we set observational constraints of the superfluid Chaplygin gas model, which gives a unified description of the dark sector of the Universe as a Bose-Einstein condensate that behaves as dark energy while it is in the ground state and as dark matter when it is in the excited state. We first show and perform the various steps leading to a form of the equations suitable for the observational tests to be carried out. Then, by using a Markov Chain Monte Carlo code, we constrain the model with a sample of cosmology-independent long gamma-ray bursts calibrated using their type I fundamental plane, as well as the Union2.1 set and observational Hubble parameter data. In this analysis, using our cosmological constraints, we sketch the effective equation of state parameter and the deceleration parameter, and we also obtain the redshift of the transition from deceleration to acceleration.

Quasar correlation functions and indirect confirmation of newtonian gravity

Vasylenko O, Ivashchenko G

Cosmological tests of the Newtonian limit of gravitational theories on the basis of observational data on the large-scale structure of the Universe are discussed. We use recent issues of SDSS to study two-point correlation functions (2CF) of quasars in real and redshift space. Under assumption of local isotropy of 3-dimensional 2CF and its power-low dependence upon distances, we derive parameters of the projected 2CF and 3D 2CF of quasars (indices, amplitudes, betha parameter and bias) for scales larger than 10- 15 Mpc. Sources of errors are analyzed in detail. We use these results to constrain some alternative gravitational theories, which lead to a scale-dependent effective gravitational constant.

Dark energy description in a chiral cosmological model

Abbyazov R

Recent discovery of the Universe accelerated expansion has lead to the enormous growth of models to account of this fact. Since the canonical LCDM has problems like fine-tuning, dynamical dark energy models have been attracted a lot of attention. A chiral cosmological model was established in 1995 by S.V.Chervon. Being a model which incorporates two kinds of interactions it serves as a powerful framework of the scalar fields investigation. Since that time chiral cosmological model has been successfully used in the early Universe study and very interesting results have been obtained which are absent in the single field case. Chiral cosmological models have been suggested to be one of the possible Dark Energy models. Despite of great progress in the so called exact solutions constructing method up to recent time it was no clear understanding how to include in the models under consideration an perfect fluid. We have proposed the methods described below. The first one is a numerical integration of the ODE with some specific restrictions on the early time values of the dark energy contribution to the Universe critical density and the dark energy equation of state parameter. The second method consists in analyzing dark energy possible behaviour in terms of scale factor. Specify- ing an ansatz one can both integrate the chiral field equations and confront the model under investigation to the observational data.

107 A search for concentric rings with unusual variance in the cmb maps

Bielewicz P, Wandelt B, Banday A

We show results for the search for concentric rings with unusual variance in the 7-year Wilkinson Mi- crowave Anisotropy Probe (WMAP) data. We re-analyse claims concerning the unusual variance profile of rings centred at two locations on the sky that have recently drawn special attention in the context of the conformal cyclic cosmology scenario proposed by R. Penrose. We extend this analysis to rings with larger radii and centred on other points of the sky. Using the fast convolution technique enables us to perform this search with higher resolution and a wider range of radii than in previous studies. We show that for one of the two special points rings with radii larger than 10 degrees have systematically lower variance in comparison to the concordance lambda cold dark matter model predictions. However, we show that this deviation is caused by the multipoles up to order l = 7. Therefore, the deficit of power for concentric rings with larger radii is yet another manifestation of the well-known anomalous CMB distribution on large angular scales. Furthermore, low- variance rings can be easily found centred on other points in the sky. As such our results are not consistent with the conformal cyclic cosmology scenario.

Deep redshift topological lensing: 3-torus strategies

Roukema B

The 3-torus Friedmann-Lemaitre-Robertson-Walker cosmological model whose orientation and size are found from cosmic microwave background data using the optimal correlation method implies matched discs of topologically lensed extragalactic objects at redshifts z ∼ 6. This is the redshift range which will be extensively explored with the upcoming generation of telescope/instrument combinations. A successive filter method for collecting matched quadruples is applied to real and simulated data using the presently known parameters of the model. For 400 galaxies observed in a pair of 200 sq.deg surveys with photometric redshift errors of 0.02 over 4 < z < 7, the expected rejection of the model or detection of candidate multiply imaged objects is at the 5% significance level.

Baos and non-linearities - a 3d spherical analysis

Pratten G, Munshi D

The Baryon Acoustic Oscillations (BAO) are features in the matter power spectrum on scales of order 100 − 150 h−1 Mpc that promise to be a powerful tool to constrain and test cosmological models. The BAO have attracted such attention that future upcoming surveys have been designed with the BAO at the forefront of the primary science goals. Recent studies have advocated the use of a spherical-Fourier Bessel (SFB) expansion for future wide field surveys that cover both wide and deep regions of the sky necessitating the simultaneous treatment of the spherical sky geometry as well as the extended radial coverage. We present an extended analysis of the BAOs using the SFB formalism by taking into account the role of non-linearities in the oscillations observed in the galaxy power spectrum. The SFB power spectrum has both radial and tangential dependence and it has been shown that in the limit that we approach a deep survey the SFB power spectrum is purely radial and collapses to the Cartesian Fourier power spectrum. We discuss how this radialisation of information holds when including non-linear features.

108 New cosmological model and observational data interpretation

Vlahovic B

The paradigm of LambdaCDM cosmology works impressively well and with the concept of inflation it explains the universe after the time of decoupling. However, there are still a few concerns; after much effort there is no detection of dark matter and there are significant problems in the theoretical description of dark energy. We will consider a variant of the cosmological spherical shell model, within FRW formal- ism and will compare it with the standard LambdaCDM model. We will show that our new topological model satisfies cosmological principles and is consistent with observed data, the supernovae luminosity distance SNe Ia and CMB, but that it may require new interpretation for some data. Considered will be constrains imposed on the model by the data, as for instance the range for the size and allowed thickness of the shell. Dynamics of the shell model will be discussed and its impact on the interpretation of the comoving radius of the visible universe and interpretation of the CMB data. One prediction of this model is interpretation of the uniformity of the CMB without inflation scenario.

109 B6 - Theoretical/mathematical cosmology

Oral session

Black holes, baby universes and separate universes

Carr B, Harada T

We address the issue of whether a positive-curvature region in the early universe can have a maximum size without out being a closed universe separate from our own. The traditional approach to this problem has been questioned in recent work by Kopp et al. We agree with their analysis but claim that their criticism of our earlier work mainly involves issues of interpretation and does not invalidate the notion of a separate-universe scale. We calculate this scale for all equations of state of the form p = kρ with −1 < k < 1. For −1/3 < k < 1, the maximum size is always of order the cosmological particle horizon size, with a numerical factor depending on k. This confirms that a primordial black hole cannot be much larger than the particle horizon at formation. For −1 < k < −1/3, the situation changes radically in that a sufficiently large positive-curvature region produces a baby universe rather than a black hole but there is still a separate-universe scale. In order to make the notion of a black hole and a baby universe in a cosmological background more precise, we analyse the nature of the trapped surfaces in these models.

Generating matter inhomogeneities from spikes

Lim W

We discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early Universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that naturally occur in the initial oscillatory regime of general cosmological models. In particular, we explicitly show that spikes occurring in a class of G2 models lead to inhomogeneities that, due to gravitational instability, leave small residual imprints on matter in the form of matter perturbations. The residual matter overdensities from recurring spikes are not local but form on surfaces. We discuss the potential physical consequences of the residual matter imprints and their possible effect on the subsequent formation of large-scale structure.

110 Measure and probability in cosmology

Schiffrin J , Wald R

General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. A number of authors have used the restriction of this measure to the space of homogeneous and isotropic universes with scalar field matter (minisuperspace) - namely, the Gibbons- Hawking-Stewart measure - to make arguments about the likelihood of inflation. We argue here that there are at least four major difficulties with using the measure of general relativity to make probability arguments in cosmology: (1) Equilibration does not occur on cosmological length scales. (2) Even in the minisuperspace case, the measure of phase space is infinite and the computation of probabilities depends very strongly on how the infinity is regulated. (3) The inhomogeneous degrees of freedom must be taken into account even if one is interested only in universes that are very nearly homogeneous. The measure depends upon how the infinite number of degrees of freedom are truncated, and how one defines ”nearly homogeneous”. (4) In a universe where the second law of thermodynamics holds, one cannot make use of our knowledge of the present state of the universe to ”retrodict” the likelihood of past conditions.

A gravitational entropy proposal

Clifton T

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free grav- itational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis.

Cosmological models with a non-zero bang time function

Bolejko K

Within exact inhomogeneous cosmological models such as the Lemaitre-Tolman or Szekeres model, the Big Bang does not have to be a simultaneous event, and can occur at different places, at different times. This phenomenon is described by so the called bang time function. Cosmologists often assume that bang time function is strictly zero, and try to justify this assumption using a conjecture that non-zero bang time function would imply large inhomogeneities in the early universe, which seems to be in contradiction with inflationary scenarios. During my talk I will show how within models that have a simultaneous Big Bang or an inflationary period and highly homogeneous stage afterwards, non-zero values of the bang time function can be generated. I will also discuss what implications this non-zero bang time function can have for conditions in the early Universe.

111 Drift of light rays induced by nonsymmetric flow of the cosmic medium

Krasi´nskiA, Bolejko K

Investigation of null geodesic equations in the Szekeres models shows that observers in favourable posi- tions would see galaxies drift across the sky at a rate of up to 10−6 arc seconds per year. Such a drift would be possible to measure using devices that are under construction; the required time of monitoring would be ≈ 10 years. This effect is zero in the FLRW models, so it provides a measure of inhomogeneity of the Universe.

A virialisation-induced physical explanation for dark energy

Roukema B

By definition, the standard, homogeneous models of the Universe are likely to fail when the Universe is inhomogeneous. The virialisation fraction measures inhomogeneity. Its redshift evolution roughly matches the evolution of would-be ”dark energy”, if the ”dark energy” is inferred from the observations by assuming a homogeneous model. This suggests that ”dark energy” is a misinterpretation of the fact that we live in the inhomogeneous epoch of the Universe. A virialisation-induced approximation of an effective metric is proposed to improve the accuracy of the homogeneous models, while making them less precise.

Invariant characterization of density growing and decaying mode in ltb and szekeres models

Sussman R

Exact expressions are derived for the density growing and decaying modes of LTB and Szekeres dust models by expressing their energy density as an exact perturbation of its quasi-local volume average. The resulting expressions provide a fully covariant interpretation of the ”Goode-Wainwright” variables and reduce to the expected sum of modes of linear perturbation theory in the linear limit. The expected dominance of the decaying (growing) mode in the early (late) time evolution is revealed by looking at the evolution of the models through a dynamical system whose phase space is parametrized by the models themselves. In particular, we show that both modes co-exist but the growing mode also dominates in the collapsing stage, with conditions near the collapsing singularity being qualitatively different from those in the initial singularity. The conditions for absence of shell crossings, sign conditions on the modes and type of density profiles (clump or void) define inter-related invariant subspaces of the dynamical system. Special models with suppressed decaying mode emerge from an Einstein de Sitter attractor associated with early times homogeneity, but if they collapse their late time state is highly inhomogeneous.

Covariant perturbations of ltb spacetimes

Pratten G, Clarkson C

In this talk we present a covariant decomposition of Einstein’s Field Equations as applied to the Lemaˆıtre- Tolman-Bondi (LTB) spacetime. Based on the 1+3 covariant approach of Ellis and Ehlers, the 1+1+2 semi-tetrad approach of Clarkson and Barrett (2003) allows us to investigate perturbations of the LTB

112 model in a covariant and gauge-invariant manner. We discuss recent results in deriving master vari- ables and the corresponding set of master equations (in analogy to the Regge-Wheeler equations in the Schwarzschild spacetime) and how the results relate to the current literature, such as results derived us- ing the 2+2 formalism as presented in Clarkson, Clifton and February (2009). We also highlight future applications of interest.

Timescape cosmology: modifying the geometry of the universe

Wiltshire D

The timescape cosmology is a viable testable alternative to homogeneous models with smooth dark energy. It revisits foundational questions relating to the definition of gravitational energy in the compli- cated geometry of nonlinear structures that we observe on scales below 100/h Mpc. Cosmic acceleration is realized as an apparent effect due to the relative calibration of clocks and rulers between observers who interpret cosmological observations in terms of different average smooth geometries based on their own regional spatial curvature. In particular there is a systematic difference between observers in denser regions where structures form, relative to the volume-average expansion which is dominated by voids. In this talk I will briefly outline the present observational status of the timescape model, and more broadly discuss the challenges in developing it from a phenomenological model to a fully-fledged modified statis- tical geometrical description of the universe.

Effects of inhomogeneities on apparent cosmological observables: ”fake” evolving dark energy

Romano A, Sasaki M, Starobinsky A

Using the exact Lemaitre-Bondi-Tolman solution with a non-vanishing cosmological constant , we inves- tigate how the presence of a local spherically-symmetric inhomogeneity can affect apparent cosmological observables, such as the deceleration parameter or the effective equation of state of dark energy (DE), derived from the luminosity distance under the assumption that the real space- time is exactly homoge- neous and isotropic. The presence of a local underdensity is found to produce apparent phantom behavior of DE, while a locally overdense region leads to apparent quintessence behavior. We consider relatively small large scale inhomogeneities which today are not linear and could be seeded by primordial curvature perturbations compatible with CMB bounds. Our study shows how observations in inhomogeneous uni- verse with initial conditions compatible with the inflationary beginning, if interpreted under the wrong assumption of homogeneity, can lead to the wrong conclusion about the presence of fake evolving dark energy instead of a cosmological constant.

Averaging the luminosity redshift relation: from theory to observations.

Marozzi G

In this talk I will show a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Afterwards, using such formalism, together with adapted ”geodesic light-cone” coordinates, I will show as different effects emerge in the evaluation of observables related to the luminosity distance-redshift relation in an inhomogeneous Universe. To con- clude, considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin, I will show the magnitude and behaviour of such different effects. Our main conclusions are that such inhomogeneities cannot avoid the need for dark energy. However, taking into account the appropriate

113 corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision.

Building discrete cosmology

Rosquist K

Constructing cosmology with discrete sources represents a new step in the quest towards a description of cosmological dynamics which avoids the simplifying assumptions of the homogeneous fluid models. This approach entails a robust framework that throws new light on the outstanding problem in relativistic cosmology to understand how the small scale inhomogeneities of the real universe affect the expansion of the universe. In this note we report on recent advances in handling the mathematics of discrete models as well as drawing some striking physical conclusions. In particular, it is shown that there can be several regions in an inhomogeneous universe which are almost flat in a precise sense throughout the evolution.

Periodic lattices of black holes as inhomogeneous cosmological models

Korzy´nskiM

I will discuss vacuum spacetimes with regular, periodic lattices of black holes as the only source of the gravitational field. These spacetimes are supposed to generalize the flat, open and closed dust Friedman- Lemaitre-Robertson-Walker solutions to situations when the matter sources are strongly localized rather than homogeneous. Despite the lack of complete homogeneity they do retain a discrete group of isometries and therefore can be considered homogeneous on large scales. They form excellent models for probing the effects of large, non-linear inhomogeneites on small scales on the large-scale dynamics of the cosmological model. In my talk I will present the methods of construction of exact initial data for these spacetimes, dis- cuss their properties and present the results of their numerical evolution. In particular I will focus on comparison between the dynamics of these models and of those of the corresponding FLRW solutions.

114 Poster session

Archimedean-type interaction in a cosmic dark fluid: multistage universe history, big rip, little rip, cyclic solutions

Balakin A, Bochkarev V

We consider a new self-consistent model, the key element of which is an Archimedean-type coupling between two constituents of the cosmic dark fluid: dark matter and dark energy. We suppose that the dark matter particles are affected by the force proportional to the four-gradient of the dark energy pressure. The Archimedean-type coupling is shown to play the role of an effective energy - momen- tum redistributor inside the dark fluid, thus providing the cosmological evolution to have a multistage character. We classified the submodels with respect to a number of transition points, which appear in the model as zeros of the acceleration function, q(t), and describe the moments in the universe history, when the epochs of accelerated expansion replace the epochs of decelerated expansion. The model is investigated analytically, numerically and qualitatively. Special attention is focused on the exact solution of the anti-Gaussian type: it describes the late-time accelerated expansion of the little rip type and is nonsingular in the early universe. We show that the Archimedean-type coupling protects the universe from the big rip scenario. Based on the papers: A.B. Balakin and V.V. Bochkarev. Phys. Rev. D 83, 024035 (2011); Phys. Rev. D 83, 024036 (2011); Phys. Rev. D 87, 024006 (2013).

Electrostriction and magnetostriction in a cosmic dark fluid, and unlighted epochs in the universe history

Dolbilova N , Balakin A

We consider the model based on the Lagrangian extended by a cross-invariant, which is quadratic in the Maxwell tensor and linear in the pressure tensor of the dark fluid. Keeping in mind the analogy with classical electrodynamics of continuous media, we assume that this part of the Lagrangian describes the phenomena known as electrostriction and magnetostriction. We formulate the extended master equations, study the structure of the linear response tensor and consider cosmological examples. In the framework of isotropic cosmological model we investigate in detail the problem of propagation of electromagnetic waves influenced by the electrostrictive and/or magnetostrictive dark fluid, and describe the so-called unlighted epochs in the universe history, when the square of the effective refraction index is negative. In this context we analyze the phase and group velocities of the electromagnetic waves for three examples of the dark energy pressure, which refer to the LambdaCDM model, to the dark energy model with time-dependent effective equation of state, and to the model of Archimedean-type interaction between the dark energy and dark matter. References 1. A.B. Balakin. Gravitation and Cosmology, 13, 163 (2007). 2. A.B. Balakin, V.V. Bochkarev and J.P.S. Lemos. Phys. Rev. D 85, 064015 (2012).

Torsion and problems of standard cosmology

Hamad H

The field equation of orthodox general relativity are written in the context of a geometry with non- vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological applications. The resulting dynamical equations are those of FRW- Standard cosmology, which have many problems e.g. singularity, particle horizons, ...etc. We suggest a

115 new scheme for investigating the effect of torsion on the dynamics of FRW-Cosmology, without changing the basic structure of general relativity. It is shown that some of these problems will disappear if the torsion, associated with AP-structure used, is inserted in to the dynamical equations. Diagnose shows that problems arise when GR is written in the context of a geometry with vanishing torsion, the Riemannian geometry. This reflects the importance of using more wider geometries in studying physical phenomena.

Dbi galileon and late time acceleration of the universe

Sen A

We consider 1 + 3 dimensional maximally symmetric Minkowski brane embedded in a 1 + 4 dimensional maximally symmetric Minkowski background. The resulting 1 + 3 dimensional effective field theory is of DBI (Dirac-Born-Infeld) Galileon type. We assume the galileon field to be initially frozen due to large Hubble damping and that it behaves like a cosmological constant. However, with time the field slowly thaws out from the frozen state and starts deviating from w = −1. The deviation depends on the initial value of the slope of the potential. For smaller values of the initial slope, the evolution for all the potentials remain close to ΛCDM throughout. As one increases the value of initial slope, the evolution start deviating from ΛCDM. We study the degeneracies for the different potentials using the statefinder hierarchies. Finally we constrain our model parameters using the recent observational data. We show that larger contribution from standard canonical part results in larger deviation from ΛCDM behaviour whereas larger contribution contribution from galileon part restricts the models to behave more close to ΛCDM. This is true for all the potentials.

Realistic cosmological scenario with non-minimal kinetic coupling

Sushkov S

We investigate cosmological scenarios in the theory of gravity with the scalar field possessing a non- minimal kinetic coupling to the curvature. It is shown that the kinetic coupling provides an essentially new inflationary mechanism. Namely, at early cosmological times the domination of coupling terms H t in the field√ equations guarantees the quasi-De Sitter behavior of the scale factor: a(t) ∝ e κ with −74 2 Hκ = 1/ 9κ, where κ ' 10 sec is the coupling parameter. The primary inflationary epoch driven −35 by non-minimal kinetic coupling comes to the end at tf ' 10 sec. Later on, the matter terms are dominating, and the universe enters into the matter-dominated epoch which lasts approximately −1 18 0.5H0 ∼ 0.5 × 10 sec. Then, the cosmological term comes into play, and the universe enters into the HΛt p secondary inflationary epoch with a(t) ∝ e , where HΛ = Λ/3. Note that the present value of the 2 acceleration parameter q =aa/ ¨ a˙ is estimated as q0 ' 0.25, that is the universe is at the beginning of the epoch of accelerated expansion. Thus, the cosmological model non-minimal kinetic coupling represents the realistic cosmological scenario which successfully describes basic cosmological epochs and provide the natural mechanism of epoch change without any fine-tuned potential.

Constraining the growth factor with general relativistic effects

Guarnizo Trilleras A

Future galaxy surveys will provide new opportunities to verify the current standard cosmological model, and also to constrain modified gravity theories invoked to explain the present accelerated expansion of the universe. Recent works have been computing the quantity which is effectively measured in a galaxy

116 survey, showing that effects as redshift-space distortions and volume perturbations become relevant in the galaxy power spectrum. The main idea is to take into account the relativistic corrections to constrain the growth and explore their importance for future galaxy surveys (in particular Euclid), using Fisher matrix formalism.

Magnetized bulk viscous fluid cosmological model in general relativity

Bagora A, Purohit R

Two tilted Bianchi type IX cosmological models filled with dust fluid of perfect fluid and heat conduction in presence of magnetic field and bulk viscosity are investigated. To get determinate solution, it has been assumed that the universe is filled with pressure less fluid i.e. p=0 together with A =B , where A, and B are metric potentials. The coefficient of bulk viscosity is assumed to be power function of mass density. It has been shown that tilted nature of the model is preserved due to magnetic field. The various physical and geometrical aspects of the models are discussed. The nature of the models in presence and absence of magnetic field and bulk viscosity are also discussed.

Off-diagonal ekpyrotic cosmolgical solutions in massive gravity and effective einstein spaces

Vacaru S

We show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordi- nates can be constructed in massive gravity using the so-called anholonomic frame deformation method. There are found new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. Such solutions describe the late time acceleration due to effective cosmo- logical terms induced by nonlinear off-diagonal interactions and graviton mass. The cosmological metrics and related St¨uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaˆıtre-Robertson-Walker (FLRW) coordinates. The solutions include possible matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and coefficients of metrics, which may explain various dark energy and dark matter effects. There are stated the conditions when such configurations mimic interesting so- lutions in general relativity and recast the general Painlev´e-Gullstrandand FLRW metrics. We conclude that cosmic accelertion and certain dark energy/matter effects can be explained by off-diagonal inter- actions in Einstein gravity. Finally, we sketch a reconstruction structure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes.

Extended inflation with torsion

Wang C , Wu Y

Extended inflation successfully solved the graceful exit problem in the old inflationary model. However, it is inconsistent with the current astrophysical bound on Brans-Dicke parameter (ω > 40000). To resolving this inconsistency, we study the extended inflation in Riemann-Cartan space-times, and obtain general torsion solutions, which are completely determined by Brans-Dicke scalar field Φ, in the false vacuum energy dominated epoch. The substitution of the torsion solutions back to the action gives the original Brans-Dicke action with Φ-dependent Brans-Dicke parameter ω(Φ). The evolution of Φ yields that ω(Φ) asymptotically approaches to infinity, which is consistent with the current solar-system observations. To understand the constraint of bubble-size distributions on ω(Φ), we calculate the bubble nucleation rates

117 in this extended inflationary model with torsion. Other cosmological bounds, e.g. primordial power spectrum of the density perturbation, on this model are also discussed.

Unorthodox solutions of einstein equations for description of dark matter

Gallo E, Geser F, Moreschi O

An unsolved problem in the study of dark matter is that when using different techniques; as for example, dynamical studies of galaxies in a cluster, and weak lensing on background images; one find no coincidence in the mass content of the galaxy cluster. In a previous study of weak lensing we have noticed that a spacelike contribution of the energy-momentum tensor has been neglected in standard works by further assumptions. Motivated by this, we have shown exact solutions of the field equations, which are static and spherically symmetric, with no mass content, but with a non-vanishing spacelike components of the stress-energy-momentum tensor; which describe the main aspects of dark matter phenomena. In this work we improve on this model by including an energy-momentum tensor whose mass content matches the predictions of dynamical studies of a cluster of galaxies and also adjusts for the weak lens description of the images in the background. We will comment on the peculiar spacelike components of the energy-momentum.

Scalar-tensor and multiscalar-tensor cosmology in the general relativity limit

Jarv L, Kuusk P, Saal M, Randla E

We consider Jordan frame scalar-tensor gravity with arbitrary potential and coupling functions in flat FLRW cosmological spacetimes, in the dust matter and potential dominated epochs. We develop and apply an approximation scheme in the regime close to the so-called limit of general relativity and solve the ensuing nonlinear equations for the scalar field and Hubble parameter analytically in cosmological time. This allows us to distinguish the theories with solutions that asymptotically converge to general relativity and draw implications about the cosmological dynamics near this limit. Further, we also apply these methods to the generalized case with multiple scalar fields.

Issues concerning loop corrections to the primordial power spectra

Miao S

We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field ζ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter ∈. We propose an extension which should be better behaved.

118 The stability of bianchi space-times with positive cosmological constant and the cosmic-no-hair conjecture

Luebbe C , Mena F

In this talk we discuss the late time behaviour of spacetimes that are initially expanding, initially close to a class of Bianchi spacetimes (not type IX) and satisfy the Einstein field equations for a radiation fluid or an Einstein-Maxwell system with a positive cosmological constant. We prove that in the long term these almost spatially homogeneous spacetimes locally approach deSitter space at late times and thus satisfy the cosmic-no-hair conjecture. This work generalises the result of Wald (1983) for exact spatially homogeneous spacetimes.

Evolution of the entropy of the universe between inflation and the far future

Pavon D, Mimoso J

Assuming the Universe behaves as any ordinary thermodynamic system, the evolution of its entropy between the initial inflationary era and the asymptotic far future is studied. We use two recently proposed cosmological models that cover the whole expansion history (Phys. Rev. D 86, 103534 (2012), and MNRAS (2013) doi:10.1093/mnras/stt220). Both models start with an initial de Sitter expansion, go through the conventional radiation and matter dominated eras to be followed by a final and everlasting de Sitter expansion. In spite of their outward similarities (from the observational viewpoint they are arbitrary close to the conventional Lambda cold dark matter model), they deeply differ in the physics behind them. Our study reveals that in both cases the Universe approaches thermodynamic equilibrium in the last de Sitter era in the sense that the entropy of the apparent horizon plus that of matter and radiation inside it increases and is concave. Cosmological models that do not approach equilibrium at the last phase of their evolution appear in conflict with the second law of thermodynamics. We then discuss why we believe our starting assumption is correct. Details can be found in Phys. Rev. D 87, 047302 (2013), and Gen. Relativ. Grav. 45, 63 (2013).

Reducing phase space of the bianchi ix model

Czuchry E

The mathematical structure of higher dimensional physical phase spaces of the non-diagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical systems methods. Critical points of the Hamiltonian equations appear at infinities and are of a nonhyperbolic type, which is a generic feature of considered singular dynamics. The reduction of the kinematical symplectic 2-form to the constraint surface enables determination of the physical Hamiltonian. This procedure lowers the dimensionality of the dynamics arena. The presented analysis of the phase space is based on canonical transformations. We test our method for the specific subspace of the physical phase space. The obtained results encourage for making further examination of the dynamics within our approach.

Perturbations in loop quantum cosmology

Nelson W

I will present a general method of evolving quantum perturbations on a quantum background, focusing, as a specific example, on Loop Quantum Cosmology. I will review the underlying classical description of

119 linear cosmological perturbations and explain how this can be quantised. I will then demonstrate this approach by showing the power spectra produced during inflation and discussing the consistency of the approximations.

Holographic dark energy

Zimdahl W , del Campo S, Fabris J, Herrera R

Holographic DE models are based on a field theoretical relation between cutoffs in the ultraviolet and in the infrared energy regions. Different choices of the infrared cutoff give rise to different models. We compare models for which the Hubble scale, the future event horizon or a quantity proportional to the Ricci scale are taken as the infrared cutoff length. The mere definition of the holographic dark-energy density is shown to imply, in general, the existence of an interaction with the dark-matter component. We discuss the relation between the equation-of-state parameter and the energy density ratio of both components for each of the choices, as well as the possibility of non-interacting and scaling solutions. Special attention is devoted to Ricci dark energy. We demonstrate that the requirement of separate energy-momentum conservation of the components establishes a relation between the matter fraction and the (necessarily time-dependent) equation-of-state parameter of the dark energy. This makes it an observationally testable alternative to the ΛCDM model. Singling out intrinsically adiabatic pressure per- turbations of the dark-energy component, the matter perturbations are found, within a gauge-invariant analysis, as linear combinations of the total energy-density perturbations of the cosmic medium and the relative (non-adiabatic) perturbations of the components.

Merging gravitation with thermodynamics to understand cosmology

Bondarescu M , Lundgren A, Bondarescu R

We discuss the evolution of the universe in the context of the second law of thermodynamics from its early stages to the far future. Cosmological observations suggest that most matter and radiation will be absorbed by the cosmological horizon. On the local scale, the matter that is not ejected from our supercluster will collapse to a supermassive black hole and then slowly evaporate. The history of the universe is that of an approach to the equilibrium state of the gravitational field. We further discuss the need for a consistent definition of gravitational entropy when there is not black hole horizon present. We review quasi-local quantities, which allow us to define energy and ultimately entropy in the framework of General Relativity. We then use Brown York quasi-local quantities to compute the entropy inside a star.

Explorations of effective pgt lagrangian of the spin-0 dynamical connection modes in the isotropic bianchi v cosmology

Chen H , Nester J

Previous investigations of the Poincar’e gauge theory found two well behaved dynamic connection modes, which are scalar modes with spin−0+ and spin−0−. The dynamics of these modes in some cosmological models has been investigated. We found that these two modes could account for the presently accelerating universe. A manifestly homogeneous Bianchi representation has been applied to a more general BHN PG model; we found that the effective Lagrangian analysis is not only valid in the isotropic Bianchi class A (type I, type IX) cases but also in the isotropic Bianchi class B (type V) case.

120 The role of the material spin density in torsion cosmology has been reconsidered in this work. We argue that the spin density does not directly drive the dynamic scalar modes.

An alternative method for linear cosmological perturbation analysis

Musco I

This talk will present an alternative method for characterizing the linear growth of cosmological pertur- bations in the early universe, corresponding to a pure growing mode, when perturbation length-scales are much larger than the cosmological horizon. In this regime, pressure gradients are second-order effects and the curvature perturbation can be characterized by a constant profile. Using the spherical Einstein hydrodynamical equations, within the context of an FRW background, the self-similar growth of cosmo- logical perturbations can be described by specifying only the initial radial profile for the curvature. In this way, one can get a complete set of initial conditions for use in numerical cosmological simulations. In the case of an initially pressureless dust background, this description is valid also within the cosmological horizon, and we will discuss the importance of then considering a non-zero pressure (corresponding to a non-zero effective temperature of the particles) in the subsequent non-linear evolution.

Linking cosmic holography, spacetime curvature, and virtual gravitons: a proposed model for dark energy

Bryja C

We derive a remarkably successful prediction for the value of the cosmological constant from three postu- lates: Bousso’s (2002) conjecture that the holographic bound of the universe is saturated at the observer’s apparent horizon is correct; Gibbons & Hawking’s (1977) conjecture that the event horizon seen by an observer within a de Sitter universe is physically equivalent to the event horizon of a Schwarzschild black hole is true in all respects for horizons of identical surface area; and, all present components of vacuum energy sum to zero except for one purely curvature-dependent component that effectively can be modeled as a dark energy fluid with a dynamic equation of state. We show that the consequent time evolution of dark energy predicted by these postulates is viable within current observational constraints. While the derivation involves no quantum physics other than what is manifest in the holographic principle, it also is consistent with a model in which the dark energy consists of uncancelled ultra-low energy virtual gravitons that have wavelengths and Heisenberg lifetimes extended indefinitely by the expansion of space. In this model, the homogeneous energy density of these immortal virtual gravitons remains directly proportional to global cosmic curvature: increasing with time when limited by their mean free paths in a matter or radiation filled universe, then encountering the holographic limit when the graviton quanta ultimately reach cosmological dominance.

Cosmological perturbations of a quartet of scalar fields

Koh S

We consider the linear perturbations for the single scalar field inflation model interacting with an ad- ditional triad of scalar fields. The background solutions of the three additional scalar fields dependent on spatial coordinates with a constant gradientand the ensuing evolution preserves the homogeneity of the cosmological principle. We find that cosmological observable quantities such as the power spectrum, spectral indices of scalar and tensor perturbations, and the running of the spectral indices have small cor- rections depending on the lower bound of comoving wavevector which is introudced to have well-defined initial quantum states.

121 Moments of the universe

Dautcourt G

If the universe is infinite in its spatial extension, its description in terms of specific cosmological solutions (such as FLRW, LTB or Szekeres, for example) could be in error at large distances. It appears reasonable to discuss also local models, which give an adequate description only within and slightly outside the Hubble volume. A way to do so was suggested in 1985 by Xia-He Zhang, who used time-dependent multipole moments to characterize the gravitational influence of the external universe. His method may be considered as another form of gradient expansion or as extension of the Kristian-Sachs 1966 procedure towards time-dependent expansion coefficients. We follow these ideas and specify what is meant by assuming that our spacetime corresponds to a flat Lambda-FLRW model near the worldline of an (geodesic) observer. We then carry out a Taylor expansion around this worldline and compare solutions of the resulting field equations for the moments with cosmological observations.

Forecasting model-independent observables in dark energy cosmologies

Guarnizo Trilleras A

The effective anisotropic stress or gravitational slip η = −Φ/Ψ is a key variable in the characterisation of the physical origin of the dark energy, as it allows to test for a non-minimal coupling of the dark sector to gravity in the Jordan frame. It is however important to use a fully model-independent approach when measuring η to avoid introducing a theoretical bias into the results. In this work we forecast the precision with which future large surveys can determine η in a model-independent way that only relies on directly observables quantities.

Quantum correlations across the de Sitter horizon

Alonso Serrano A, Luis J. Garay LJ, Mena Marugn GA

We construct a minisuperspace model for de Sitter space, in order to consider the different regions of the analytically extended spacetime, some of them being interpretable as Kantowski-Sachs Universes. We construct the kinematical Hilbert space of quantum states for each region and obtain the solutions of the Wheeler-de Witt equation for this extended spacetime. In this way we determine the physical Hilbert space that allows us to relate all such regions through the horizons, using the fact that a global arrow of time can be established. We study the quantum influence of those separate classically-disconnected spacetime regions by means of the observable trace left in one region by the others, and comparing the result with the case without correlations.

122 C1 - Pulsar Timing Arrays: Latest Developments and Future Directions

Oral session

Probing massive black hole binaries with pulsar timing arrays

Sesana A

Pulsar timing arrays (PTAs) provide a promising tool to probe massive black hole binaries in the low redshift Universe. The strength of the emitted gravitational wave signal depends on several crucial parameters of the binary population, namely their masses and their space density. I will discuss how the signal depend on such parameters and what we can learn about these elusive objects with PTA observations in the near future.

Gravitational wave detection with the european pulsar timing array

Perrodin D

Pulsar timing arrays are promising laboratories for the detection of gravitational waves. The high precision timing of an array of millisecond pulsars in our galaxy could indeed enable us to detect a background of gravitational waves coming from supermassive black hole binaries. Here we describe the efforts of the European Pulsar Timing Array (EPTA) collaboration in achieving the high precision timing necessary for gravitational wave detection. We also outline the efforts of the Large European Array for Pulsars (LEAP) project, which seeks to coherently add millisecond pulsar data from 5 large European radio telescopes. Finally we outline progress at the Sardinia Radio Telescope, a new large telescope key to EPTA and LEAP efforts.

123 Searches for a stochastic gravitational wave background with pulsar timing arrays: a data analysis pipeline

Chamberlin S, Creighton J, Demorest P, Ellis J, Price L, Romano J, Siemens X

Pulsar timing arrays are a promising tool for probing the universe through gravitational radiation. Supermassive black hole binaries (SMBHBs), cosmic strings, relic gravitational waves from inflation, and first order phase transitions in the early universe are expected to contribute to a stochastic background of gravitational waves (GWs) in the pulsar timing array (PTA) frequency band of 10( −9) Hz to 10( −7) Hz. Here, we present a fully functional data analysis pipeline for the detection of a stochastic background of gravitational waves in the PTA band. We describe the underlying statistics of our method and discuss the inherent challenges in stochastic GW searches. We provide a robust frequentist upper limit for the signal size detectable with this pipeline. We also present preliminary results obtained in this pipeline for the International Pulsar Timing Array (IPTA) Mock Data Challenge, and discuss future implications and limitations.

Angular resolution and geometrical dependence of a pulsar timing array to detect individual gravitational wave sources

Wen L

An array of well-timed and well-behaved millisecond pulsars can be used to detect nanoHertz gravitational waves (GWs) by measuring the pulse arrival time fluctuation caused by the presence of the GW. The most sensitive search will come from an optimal combination of all available pulsar timing data. I’ll present analytical expressions for (1) the angular resolution of a pulsar timing array (PTA) for individual GW sources, and (2) the effect of geometrical distribution of the pulsars involved on PTA’s response to the two GW polarizations. I’ll discuss the implication of our result.

Continuous gravitational wave search methods and results from pulsar timing arrays

Ellis J

Pulsar timing arrays (PTAs) offer a unique opportunity to detect low frequency GWs in the near future. In this frequency band, the expected source of GWs are Supermassive Black Hole Binaries (SMBHBs) and they will most likely form in an ensemble creating a stochastic GW background with the possibility of a few nearby/massive sources that will be individually resolvable. The data analysis problem for detecting GWs with PTAs is not dominated by the complexity of the GW waveform as these sources are far from merger and more complex corrections to the waveform are negligible. Instead the difficulty lies in the PTA data itself which is irregularly sampled, and may contain many artifacts related to a deterministic timing model that must be subtracted from the data as well intrinsic pulsar behavior that is not well understood. Here we will discuss the development of a robust continuous GW pipeline aimed at detection and characterization. We will discuss our sampling methods including parallel adaptive MCMC and parallel tempering adaptive MCMC algorithms aimed at efficient parameter estimation and calculation of the Bayesian evidence. Finally, we will show preliminary results of this search on the International Pulsar Timing Array (IPTA) datasets.

124 Probing anisotropy of the gw background and modified-gravity with pulsar timing arrays

Taylor S

The first direct detection of gravitational-waves (GW) will open up a new window onto the dark Universe. In particular, pulsar timing arrays (PTA) employ the Milky Way as a kiloparsec GW detector to probe the nHz frequency regime. The precisely measured arrival-times of signals from pulsars make them exceptional clocks, allowing us to fit a timing-model to their spindown due to EM outflow and signal- delay due to ISM dispersion, and hence infer any deviations induced by the perturbing influence of a passing GW. If we have an isotropic background with GR as the correct description of gravity, then the correlation of deviations between pulsars separated across the sky will have the very distinctive ”Hellings and Downs” signature. However if the background is instead dominated by a few single-sources, then we could search for this anisotropy through the deviations from the expected angular-correlation signature. We describe such a search, using a robust, unbiased Bayesian pipeline to search for anisotropy in simulated datasets. Furthermore, if GR is not a complete description of gravity, then we can test for the presence of extra non-Einsteinian polarisation states through deviations from the Hellings and Downs signature. We have employed Bayesian model-selection and a model-independent reconstruction of the angular-correlation to illustrate the potential of PTAs to infer finiteness in the GW background and the signature of non-Einsteinian polarisation states.

Describing anisotropy in the gravitational wave background with pulsar timing arrays

Mingarelli C , Sidery T, Mandel I, Vecchio A

Pulsar Timing Arrays are currently the only way to search for gravitational radiation in the nanohertz band. The main sources of interest are gravitational wave backgrounds generated by supermassive black hole binaries or processes in the early universe. Several limits on this background have been set in recent years and searches of increasing sensitivity are currently ongoing. All the searches so far have only been done for isotropic backgrounds. However, a level of anisotropy may be present in the background radiation, and if a stochastic signal is detected it is important to characterise its power at different angular scales. We decompose a generic anisotropic background into spherical harmonics and compute and characterise the overlap reduction functions for any pulsar pair, which is an essential element for the evaluation of the likelihood function used in searches.

Black hole hunting with pulsar timing arrays

Cornish N , Romano J

It is anticipated that within the next decade Pulsar Timing Arrays will detect the gravitational waves emitted by supermassive black hole binaries. Analyzing those signals poses an interesting challenge as the signals are neither discrete and resolvable, nor do they form an isotropic, stochastic background. Traditional analysis techniques based on either of these assumptions are sub-optimal, and will delay the first detection. I will describe a new analysis technique that has greater sensitivity to the non-Gaussian, anisotropic signals produced by a population of black hole binaries.

125 Example of generator gluing method as the application of differential spaces theory in cosmology

Drachal K ,

126 Poster session

A new method to search for supermassive black hole binaries.

Rosado P, Sesana A

We present a new technique to search for low redshift supermassive black hole binaries (MBHB), which are expected to be the main gravitational wave (GW) sources for pulsar timing arrays (PTAs). Us- ing mock galaxy catalogues from the Millennium Simulation, we investigate the peculiar properties of merging galaxies. We find that they are biased towards larger masses and redshifts, and have a distinct distribution of neighbouring galaxies below approximately 10 Mpc. Using machine learning algorithms, we demonstrate that such information can efficiently recover MBHBs in mock galaxy catalogues, as well as in catalogues adapted to the observational limitations of a real galaxy survey (namely the Sloan Digi- tal Sky Survey, SDSS). We then apply the same technique directly to the spectroscopic SDSS catalogue, assigning to each galaxy a probability of containing a MBHB. The result is a probability sky map that can be used both to perform targeted searches in particular directions of the sky (the ones with higher probability of hosting a MBHB), and to study the properties of the overall background (i.e., deviation from Gaussianity, anisotropy, etc.). The spectroscopic SDSS covers less than a quarter of the sky and becomes severely incomplete at z¿0.1; however, this technique can be applied in the future to larger catalogues, to obtain detailed observationally based information of the expected GW signal detectable by PTAs.

Recent Results from the Parkes Pulsar Timing Array Project

Shannon R

The Parkes Pulsar Timing Array (PPTA) project has been conducting regular observations of approx- imately 20 millisecond pulsars since early 2005. In this presentation, I will highlight recent results from the PPTA project. I will also present the first PPTA data release and a limit on the strength of the stochastic gravitational wave background derived from this data release. I will also discuss a new model for the GW background from massive black hole binaries based on Millennium simulations and accompanying semi-analytic models and interpret the limit in the context of this model. I will conclude by presenting algorithmic developments for searching for bursts of gravitational waves in pulsar timing datasets.

127 C2 - GWs: Search Results, Data Analysis and Parameter Estimation

Oral session

Searching for gravitational wave signals from rotating neutron stars with the ligo and virgo detectors

Bejger M , Krolak A

A brief overview of basic mechanisms of gravitational radiation from rotating neutron stars will be given with emphasis on the most recent results. Basic types of searches for gravitational wave signals - targeted searches from known pulsars, directed searches from known locations on the sky, wide parameter searches for unknown rotating neutron stars will be presented. Data anlysis methods used in all these types of investigation will be discussed. Finally the most recent results of quest for gravitational wave signals from neutron stars in the data collected by LIGO and Virgo detectors will be summarized.

Perspectives for intermediate mass black hole searches with networks of second generation ground-based detectors

Mazzolo G

Intermediate mass black holes (IMBH, masses from 102 to 105 solar masses) have been invoked to interpret several astrophysical processes. Observation of gravitational-wave (GW) radiation emitted by coalescing IMBH binaries (IMBHB) would be a compelling proof of their existence . The sensitivity of the first generation (1G) GW detectors is insufficient to measure the IMBHB merger rates predicted from astrophysical models. However, this situation is expected to change drastically in a few years with the upgrade of the LIGO and Virgo detectors and the construction of the KAGRA detector (2G detectors). Chances of IMBHB detection will be significantly increased over a wide range of binary parameter space. We estimate the sensitivity of searches for coalescing non-spinning IMBHs with networks of 2G detectors. Waveforms, which are modeling gravitational radiation from compact binaries, are added to 2G detector simulated noise and searched for with the coherent WaveBurst algorithm. Results are presented for the source-frame binary total masses ranging from 50 to 1050 solar masses and mass ratios between 1 : 6 and 1 : 1. Within the investigated parameter space, our search is sensitive to the IMBHB sources up to the Gpc range. A theoretical model including the effects of standard cosmological parameters was developed to estimate the expected observation rates, yielding few tens of events per year.

128 Inverse problem for gravitational wave transients

Klmenko S

Inverse problem - reconstruction of gravitational wave (GW) events and their parameters from signals recorded by detectors - is central in the GW data analysis. Usually it is divided in two parts: separation of GW signals from the detector noise and estimation of the signal parameters, resulting in various detection statistics and methods for the source reconstruction. However, in general, these two parts should be considered together within the same analysis framework, called coherent network analysis, which combines data from all detectors. In my talk I describe the coherent network analysis in application to detection of poorly modeled transient GW signals. It employs the sparse time-frequency representation of GW data, dual stream analysis and constraints, which address the ambiguity of the inverse problem. Also I will discuss the existing/future GW detector networks and their capabilities for detection, sky localization and reconstruction of source parameters.

Searching for cosmic strings with the ligo-virgo gravitational-wave experiments

Robinet F

Cosmic strings are linear topological defects which are expected to form during symmetry-breaking phase transitions in the early universe. In addition, some inflation models based on string theory predict that fundamental strings and D-strings could grow to cosmic scales and constitute a network of cosmic superstrings. When forming loops, cosmic strings radiate energy through bursts of gravitational waves in the presence of cuspy features. This mechanism represents one of the most promising observational signatures to detect the existence of cosmic strings. The sensitivity of ground-based gravitational-wave detectors LIGO and Virgo allows us to explore an unconstrained region of the cosmic string parameter space. After reviewing the cosmic string models and the targeted gravitational-wave signals, we present the search for cosmic string burst signals which has been conducted over 5 years of joint LIGO-Virgo data. We discuss the astrophysical impact of this search and the future prospects for the advanced detectors era.

Untangling precession to produce generic waveform models

Schmidt P, Hannam M

One of the greatest theoretical challenges in the build-up to the Advanced gravitational-wave detector era is the modelling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a 7-dimensional parameter space) can be mapped to only a two-dimensional space of non-precessing binaries, characterized by mass ratio and a single effective total spin. The mapping consists of a time- dependent rotation, and is extremely accurate (matches ¿ 0.99 with parameter biases in the total spin of less than 0.02). We outline a general proposal for the construction of precessing-binary waveform models. Further, we show that precession effects can be efficiently modelled with a small number of parameters.

129 Searching for stellar-mass binary black hole coalescences with ground-based interferometers

Dent T

Binary black holes with components in the 3 − 50 solar mass range are one of the most promising targets for ground-based interferometric gravitational wave detectors, as potentially the brightest GW sources in their sensitive frequency band. Both the properties of these binaries (masses and spins) and their coalescence rates are subject to large uncertainties; thus positive detections, or even stringent rate limits, could provide unique information allowing us to select between models of binary formation and evolution. I will present the results of searches for these binaries in the most recent joint LSC-Virgo science run; I will also discuss the science case and prospects for detection in the Advanced detector era, and technical challenges faced by current and future searches.

Stochastic gravitational wave background searches with advanced ligo and advanced virgo: strategies and goals

Christensen N

(On behalf of the LIGO Scientific Collaboration and Virgo Collaboration) The Advanced LIGO and Advanced Virgo detectors are expected to start acquiring data in 2015, and work toward their target sensitivity over the subsequent years. A major goal for LIGO and Virgo will be to detect or set limits on a stochastic background of gravitational waves. A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved cosmological and/or astrophysical sources. A cosmologically produced background would carry unique signatures from the earliest epochs in the evolution of the Universe. Similarly, astrophysical background would provide information about the astrophysical sources that generated it. Advanced LIGO and Advanced Virgo observations should be able to probe interesting regions of parameter space for these models. We will outline LIGO and Virgo’s search strategies for these signals. We will also discuss how global electromagnetic noise (Schumann resonances) will affect this search, and possible strategies to monitor and subtract this potential source of correlated noise in a the global detector network.

Seach for massive gravitational-wave background with a detector network

Nishizawa A, Hayama K

In a general metric theory of gravitation in four dimensions, six polarizations of a gravitational wave are allowed: two scalar and two vector modes, in addition to two tensor modes in general relativity. Such additional polarization modes appear due to additional degrees of freedom in modified gravity theories. Also gravitons can be massive in modified gravity theories. Here we consider a ground-based detector network and report the method that searches for such gravitational waves with additional polarization and graviton mass. We will show that the detector network is able to probe for massive stochastic grav- itational waves with its mass below 10−12eV . We also show that more than three detectors are required to separate the mixture of polarization modes in detector outputs and determine the graviton mass. Thus, testing the existence of additional polarization and graviton mass can be a model-independent test of gravity theories.

130 Parameter estimation for compact binary coalescence signals with ligo - virgo: a rehearsal for the advanced detector era

Veitch J

Compact binary systems containing neutron stars and/or black holes are one of the most promising sources for ground-based gravitational-wave detectors. Gravitational waves encode rich information about source physics. Parameter estimation and model selection are crucial analysis steps for any detec- tion candidate events. Detailed models of the anticipated waveforms enable inference on several parame- ters, such as component masses, spins, sky location and distance, that are essential for new astrophysical studies of these sources. However, accurate measurements of these parameters and discrimination of models describing the underlying physics are complicated by artifacts in the data, uncertainties in the waveform models and in the calibration of the detectors. We will report such measurements on a selection of simulated signals added either in hardware or software to the data collected by the LIGO and Virgo detectors during their most recent joint science run, including a ”blind injection” where the signal was not initially revealed to the collaboration. We will demonstrate the ability to extract information about the source physics on signals that cover the neutron-star and black-hole binary parameter space over the component mass range 1 Msun - 25 Msun and the full range of spin parameters. The cases reported in this study illustrate the status of parameter estimation in preparation for the operation of advanced detectors.

Effect of merger and ringdown signals on the estimation of parameters of binary black holes

Graff P, Buonanno A, Sathyaprakash B

In this study, we perform a Bayesian analysis of massive binary black hole systems using effective- one-body waveforms. Our waveform model includes merger and quasi-normal modes that are tuned to numerical relativity results for many spherical modes of radiation. The additional modes help determine the parameters of progenitor binaries even when their inspiral phase might not be in the sensitivity band of a detector. We show the importance of including sub-dominant spherical modes beyond the dominant (2,2) mode. We investigate the dependence of measurement uncertainty as well as biases incurred when not including higher order modes as a function of source parameters.

Tiger: a data analysis pipeline for testing general relativity with gravitational waves from coalescing binaries

Agathos M , Del Pozzo W, Li T, Van Den Broeck C, Vitale S, Veitch J

Among the most promising classes of gravitational wave sources in the advanced detector era, is that of coalescing binary systems, consisting of neutron stars and/or black holes. The detection of gravitational wave signals from such events will, for the first time, give us access to the relativistic, strong-field dynamics of gravity. We have developed TIGER, a Bayesian data analysis pipeline for the purpose of testing general relativity using gravitational wave signals from binary neutron stars, first introduced by Li et al. (2011). This framework does not rely on any particular alternative theory of gravity, is well-suited to low signal-to-noise detections, and will allow us to combine information from multiple detections in a straightforward manner. The pipeline is mature for the case of binary neutron stars, but several concerns might still be raised: What would be the effect of arbitrary, precessing spins? What would be the effect of detector calibration errors? Given the mismatch between waveform approximants for the inspiral, how does the pipeline treat simulated signals generated by different approximants and,

131 by extension, a real signal? Can neutron star tidal effects of unknown magnitude be separable from GR violations? In this work we address the above issues one by one, and demonstrate the robustness of our pipeline.

Ability of aligo to detect violations of cosmic censorship and the no-hair theorem from binary black hole inspirals

Wade M , Creighton J, Ochsner E

In anticipation of the new era of gravitational wave detectors, it is especially important to develop methods for gaining information about astrophysical systems from gravitational wave signals. We have been working on developing a method for testing the cosmic censorship conjecture and the no-hair theorem using the inspiral portion of the compact binary coalescence gravitational waveform. The cosmic censorship conjecture implies a limit on the spin to mass squared ratio of a black hole. The no-hair theorem implies that a black hole should not be tidally deformed. The method we are developing will allow us to predict advanced LIGO’s ability to detect violations of the cosmic censorship conjecture and the no-hair theorem in the Kerr geometry. We use parameter estimation techniques to calculate the measurability of the spin, mass, and tidal parameters appearing in the gravitational waveform, and then determine if the measurability of these parameters will allow for the detection of a violation of either cosmic censorship or the no-hair theorem. We have investigated the effect of limiting the parameter space to only physically allowed values of the symmetric mass ratio, and we have investigated the effect of using improved post-Newtonian models for the CBC inspiral waveform.

Towards rapid parameter estimation on cbc sources with advanced detectors

Smith R

Coalescing compact binaries, consisting of neutron stars and/or black holes are prime sources for second generation gravitational-wave observatories. Estimating the parameters of such sources in a full Bayesian framework is essential to gravitational-wave astronomy, but can be highly computationally intensive, with analyses on a single stretch of data taking up to several hundred hours. Here we showcase two techniques which may enable low latency (Bayesian) parameter estimation in the advanced detector era. These are: (i) using interpolated template gravitational waveforms as filters of the data, and (ii) directly interpolating the compact binary likelihood function. Both techniques have the potential to reduce the computational cost of parameter estimation by at least an order of magnitude. Our results have important implications for both parameter estimation and coherent searches for gravitational-waves from compact binary sources, and we discuss these in the context of second generation gravitational-wave observatories.

132 Poster session

Progress of the low latency pipeline for the gravitational wave detector mario schenberg.

Da Silva Costa C , Denis Aguiar O, Fauth A

The Mario Schenberg gravitational wave antenna located in Sao Paulo, is a spherical resonant mass detector which is 65cm in diameter weighing 1150kg. The antenna is currently being upgraded and the next run will occur later this year. Since the last run in 2008, its 6 parametric transducers, measuring the sphere quadrupolar mode oscillations, have been redesigned to increase their mechanical Q. Spherical detectors present the ability to determine simultaneously both source direction and signal polarization. We have developed a low latency pipeline that takes advantage of these abilities and process real time data in less than half the acquisition time. For each reconstructed direction its resolution and systematic error are determine using a mapping error system and to reduce the false alarm rate, triggers are vetoed using information from the spherical modes. In the near future, we expect to add a matched filter to the pipeline. This will increase GW parameter resolution and reduce the false alarm rate. As a future part of the pipeline, a cosmic ray veto was added to the Mario Schenberg setup in December 2011. Since then, it is acquiring data and we are analyzing the energy deposition due to cosmic rays on the sphere quadrupolar modes. First measurements gave values 5 orders below the expected values. New simulations are being done to understand these results. Here, we present preliminary results of the cosmic ray measurements and the low latency method per- formance.

Initial dominant spin orientations for unequal mass spinning compact binaries

Gopakumar A, Gupta A

We probe the benefits of specifying orbital and spin angular momentum vectors in an invariant frame associated with the initial direction of total angular momentum j0 while performing gravitational wave (GW) phasing for spinning compact binaries. Isolated unequal mass spinning compact binaries are evolved until their GWs enter frequency windows of interferometric detectors. We show that the dominant ◦ spin is likely to have orientations < 90 from j0 when unequal mass spinning compact binaries spiral into initial frequencies of GW observatories if the larger spin exceeds the orbital angular momentum at these frequencies. For orbital angular momentum dominated binaries, it is rather difficult to provide similar constraints on the dominant spin orientations though they are fairly likely to be in the neighborhood of the first quadrant. We demonstrate the inability of gravitational radiation reaction to constrain dominant spin orientations in the traditional GW phasing approach and attribute it to the fact that traditionally the spins are initially specified in an orbital triad. We argue that the number of templates, required to span angular sectors of associated signal manifolds, could be substantially smaller in our GW phasing prescription.

Studying the effects of tidal corrections on parameter estimation

Wade L, Ochsner E, Creighton J, Lackey B

Tidal deformations of neutron stars in binary systems during the in fall of gravitationally radiating neu- tron stars before merger call for analytic corrections to the post-Newtonian gravitational-wave waveform.

133 Tidal deformation information is important to searches for gravitational waves from these sources be- cause they can break degeneracies in the estimation of the physical parameters of the binary and could also lead to insights about the neutron star equation of state. Using full Bayesian MCMC (Markov Chain Monte Carlo) simulations, we studied how tidal corrections affect and inform parameter estimation for binary neutron stars. We also investigate the systematic biases that arise in parameter estimation from using different post-Newtonian waveform families.

Measuring the neutron-star equation of state with multiple binary neutron star inspiral events

Lackey B

Gravitational waves from compact binaries containing neutron stars can provide useful constraints on the neutron-star equation of state. In binary neutron star systems this information comes mainly from the imprint of the neutron-star tidal deformability on the waveform during inspiral. Previous work has shown that the tidal deformability is measurable with Advanced LIGO for a single event when including the tidal effect up to merger. In this work we describe a method for stacking measurements of the tidal deformability from multiple inspiral events to measure the unknown parameters of a parametrized equa- tion of state. Specifically, we use a 4-parameter piecewise polytrope that matches theoretical equation of state models to a few percent to determine the accuracy that one can measure the pressure at twice nuclear density as well as the adiabatic index in three density regions. We also examine how the uncer- tainties in the equation of state parameters depend on the number of observations and on the distribution of neutron-star masses in binary neutron star systems.

Bayeswave: sorting the wheat from the chaff

Baker P, Cornish N

A central challenge in Gravitational Wave Astronomy is the identification of weak signals in the presence of non-stationary and non-Gaussian noise. The BayesWave algorithm is adopts a holistic approach to gravitational wave data analysis that directly models both the gravitational wave signals and the non-stationary and non-Gaussian instrumental noise. Bayesian inference and model selection are used to develop posterior distributions for the signal and noise properties, and to compute odds ratios for detection.

Effect of the higher order modes of gws emitted from binary black hole mergers measured by a gw burst search algorithm

Mohapatra S, Clark J, Cadonati L

The gravitational-waves emitted from the merger of binary black holes can be expressed, as the domi- nant quadrupole modes, and sub-dominant higher order modes, in the spin-weighted spherical harmonics basis. Until now all the gravitational-wave searches that were conducted have utilized only the signal morphology of the dominant quadrupole modes for the interpretation of the search results. It is quali- tatively known that these sub-dominant modes can be crucial for certain source orientations and source parameters of the binary black holes. Recently an analytical family of binary black holes gravitational- wave signal became available. We present a study quantifying the effect of the sub-dominant modes on the expected signal-to-noise ratio measured by a morphology-independent gravitational-wave burst search.

134 Inferring core-collapse supernova physics with gravitational wave

Logue J

Stellar collapse and the subsequent development of a core-collapse supernova explosion emit bursts of gravitational waves (GWs) that might be detected by the advanced generation of laser interferometer gravitational wave observatories such as Advanced LIGO, Advanced Virgo, and KAGRA. GW bursts from core-collapse supernovae encode information on the intricate multi-dimensional dynamics at work at the core of a dying massive star and may provide direct evidence for the yet uncertain mechanism driving supernovae in massive stars. Recent multi-dimensional simulations of core-collapse supernovae exploding via the neutrino, magnetorotational, and acoustic explosion mechanisms have predicted GW signals which have distinct structure in both the time and frequency domains. Motivated by this, we describe a promising method for determining the most likely explosion mechanism underlying a hypothetical GW signal, based on Principal Component Analysis and Bayesian model selection. Using simulated Advanced LIGO noise and assuming a single detector and linear waveform polarization for simplicity, we demonstrate that our method can distinguish magnetorotational explosions throughout the Milky Way (D 10kpc) and explosions driven by the neutrino and acoustic mechanisms to D 2 kpc. Furthermore, we show that we can differentiate between models for rotating accretion-induced collapse of massive white dwarfs and models of rotating iron core collapse with high reliability out to several kpc.

A gravitational-wave search algorithm for non-precessing spinning binary black holes

Privitera S, Mohapatra S, Hanna C, Fotpolous N, Ajith P, Weinstein A, Whelan J

Previous searches for gravitational waves in LIGO-Virgo data from the inspiral, merger and ringdown of binary black holes have used a matched-filter approach with non-spinning templates. However, as- trophysical black holes in binaries are expected to have significant spin and neglecting such effects in the templates may reduce the detection efficiency. Gravitational-wave signal models from the coales- cences of non-precessing spinning binary black holes have recently become available, but it is not known whether using these templates in a search can improve detection efficiency of generic-spinning binary black holes signals in realistic, non-Gaussian noise from the Initial LIGO detectors. We present a search for gravitational-waves that employ non-precessing spinning templates and compare the performance of this search to one in which the templates neglect spin effects.

Science reach of stochastic gravitational wave background searches with second-generation detectors

Mandic V

One of the prime targets of the upcoming second-generation gravitational wave detectors will be the stochastic background of gravitational waves. The stochastic background is produced as an incoherent superposition of gravitational waves from many cosmological and astrophysical sources, and could there- fore carry unique information about cosmological and astrophysical processes that gave rise to it. I will present a new formalism designed to extract this information from the stochastic background measure- ments. The formalism offers the prospect of estimating the energy budget of the stochastic gravitational wave background, and it provides a natural framework for inclusion of other measurements to further constrain model parameters. I will also discuss applications of this formalism to some specific situations

135 - for example, to measure possible parity violation in the early universe, or to probe the stochastic background models based on coalescences of compact binaries.

Inferences from the post-merger gravitational wave signal in binary neutron star coalescence

Clark J

The inspiral phase of binary neutron star coalescence is widely considered to be one of the strongest sources in the next generation of ground based gravitational wave detectors, yielding detection rates in the range of 0.4 - 400 events per year of operation. Amongst the most exciting prospects for gravitational wave astronomy is the measurement of neutron star mass and radius, leading to constraints on the neutron star equation of state. Recent numerical simulations suggest that, rather than prompt collapse to a black hole, the favoured outcome of the merger is the formation of a relatively long-lived hyper-massive neutron star whose gravitational wave signal constitutes a significantly weaker but complementary gravitational wave source to the inspiral phase. We present results of deploying a Bayesian nested sampling algorithm in the context of a gravitational wave inspiral-triggered search for, and characterisation of, this post- merger signal.

: improved versions of the f-statistic for more efficient gw pulsar searches

Cutler C

The F-statistic is the optimal (frequentist) statistic for the detection of gravitational-wave (GW) pul- sars. However, in ”all-sky” searches for previously unknown GW pulsars, it would be computationally intractable to calculate the (fully coherent) F-statistic at every point of a (suitably fine) grid covering the parameter space. Here we describe improved versions of the F-statistic that lead to greater sensitivity at fixed computational cost. Some of the ideas here should also be useful for improving the efficiency of searches for gamma-ray pulsars in Fermi data and searches for short-period binary radio pulsars in radio data.

Impact of higher harmonics in searching for gravitational waves from binary black hole coalescence in advanced ligo

Capano C

Current searches for gravitational waves from compact binary coalescence use dominant-mode-only wave- forms as templates in a matched filter. It has been shown that neglecting additional modes causes mismatch between these templates and expected signals. We investigate the effect of this mismatch on signal-based vetoes and the detection efficiency of advanced LIGO detectors for non-spinning stellar-mass binary black holes. We also consider what improvement could be expected if a search were developed that utilized these additional modes.

Gravitational-wave parameter estimation with compressed likelihood evaluations

Canizares P, Field S, Gair J, Tiglio M

One of the main bottlenecks in gravitational wave (GW) astronomy is the high cost of performing pa-

136 rameter estimation and GW searches on the fly. We propose a novel technique based on Reduced Order Quadratures (ROQs), an application and data-specific quadrature rule, to perform fast and accurate likelihood evaluations. These are the dominant cost in Markov chain Monte Carlo (MCMC) algorithms, which are widely employed in parameter estimation studies, and so ROQs offer a new way to accelerate GW parameter estimation. We illustrate our approach using a four dimensional GW burst model embed- ded in noise. We build an ROQ for this model, and perform four dimensional MCMC searches with both the standard and ROQs quadrature rules, showing that, for this model, the ROQ approach is around 25 times faster than the standard approach with essentially no loss of accuracy. The speed-up from using ROQs is expected to increase for more complex GW signal models and therefore has significant potential to accelerate parameter estimation of GW sources such as compact binary coalescences.

Methods for the first all-sky search for continuous gravitational waves from spinning neutron stars in binary systems

Goetz E

An all-sky search for continuous gravitational waves from unknown neutron stars in binary systems is daunting in its computational challenge due to the additional binary orbital parameters that must be searched over. A new search algorithm, called TwoSpect, has been developed and implemented; it exploits the periodic orbital modulation of the source waves by searching for patterns in doubly Fourier- transformed data. This technique enables a more computationally efficient search compared to other StackSlide-like, all-sky search algorithms. We present the analysis methods and current status of the first ongoing search for sources in binary systems in the LIGO Science Run 6 and Virgo Science Runs 2 and 3 data sets.

Resolving noise structures in virgo and ligo data: an application of non-linear system identification

Piergiovanni F , Guidi G, Carini A

A gravitational-wave detector features many kinds of non-linear physical processes. Disturbances present in auxiliary channels, including narrow spectral features, may be converted linearly and non-linearly into noise polluting the gravitational channel in a wide frequency region. Uncovering such relationships between auxiliary channels and the gravitational-wave channel can be very useful to characterize the detector and possibly also to improve the confidence of gravitational-wave searches. We present a non- linear system identification tool developed to characterize linear and non-linear noise in the gravitational- wave detector output. The signal is expanded in a Volterra series of the auxiliary channels and the model parameters are determined by means of the Sorted Fast Orthogonal Search technique. Cross correlation is used to perform dephasing identification, allowing to minimize the number of time lags in Volterra expansions. The magnitude of the specific contribution of any channel or combination of channels is estimated; this gives the possibility to recognize the channels that are most involved in the noise structures, giving hints about noise sources. We applied the tool to interferometric detector data showing that it is effective to perform blind identification among several hundreds of auxiliary channels in linear and bilinear combination.

137 Gravitational waves from sco x-1 : prospects for detection and a comparison of methods

Crowder G, Dergachev V, Galloway D, Goetz E, Meadors G, Messenger C, Premachandra S, Riles K, Sammut L, Thrane E, Whelan J

The low-mass X-ray binary Scorpius X-1 is potentially our most luminous source of continuous gravi- tational wave radiation. Unlike for the recycled pulsars already targeted by LIGO-Virgo, this radiation would be powered by the accretion of matter from its binary companion rather than it’s rotational energy. With the advanced detector era fast approaching, work is underway to develop an array of robust tools for maximising the science and detection potential of Sco X-1. It will be possible with advanced detector data to attain sensitivities below the current theoretical torque-balance limits implying that signal de- tection is a possibility. We describe the plans and progress of a project designed to compare and contrast the numerous independent search algorithms currently employable. We descibe a mock-data-challenge by which the search pipelines will test their relative proficiencies in parameter estimation, search volume dependence, computational efficiency, robustness, and most importantly, search sensitivity.

Gravitational waves from sco x-1 : prospects for detection and a comparison of methods

Crowder G, Dergachev V, Galloway D, Goetz E, Meadors G, Messenger C , Premachandra S, Riles K, Sammut L, Thrane E, Whelan J

The low-mass X-ray binary Scorpius X-1 is potentially our most luminous source of continuous gravi- tational wave radiation. Unlike for the recycled pulsars already targeted by LIGO-Virgo, this radiation would be powered by the accretion of matter from its binary companion rather than it’s rotational energy. With the advanced detector era fast approaching, work is underway to develop an array of robust tools for maximising the science and detection potential of Sco X-1. It will be possible with advanced detector data to attain sensitivities below the current theoretical torque-balance limits implying that signal de- tection is a possibility. We describe the plans and progress of a project designed to compare and contrast the numerous independent search algorithms currently employable. We descibe a mock-data-challenge by which the search pipelines will test their relative proficiencies in parameter estimation, search volume dependence, computational efficiency, robustness, and most importantly, search sensitivity.

Parameter-space metric for all-sky coherent searches for gravitational-wave pulsars

Wette K , Prix R

All-sky, broadband searches for gravitational-wave pulsars are computationally limited. It is therefore important to make efficient use of available computational resources, for example by minimising the number of templates needed to cover the parameter space of sky position and frequency evolution. A difficulty is that, for searches over the sky, the required template resolution is different for each sky position, and this makes it difficult to achieve an efficient covering. Previous work on this problem has found choices of sky and frequency coordinates, with respect to which the parameter space metric (which determines the template resolution) is constant. These approaches, however, are limited to coherent integration times of a few days, which in turn limits the sensitivity achievable by e.g. a hierarchical search pipeline. We present recent work on new sky and frequency coordinates, with a flat parameter- space metric, that do not suffer from this limitation. By allowing integration times of, e.g., longer than a week, improvements in search sensitivity may be possible using the new coordinates.

138 Effect of sine-gaussian glitches on searches for binary coalescence

Dal Canton T , Bhagwat S, Dhurandhar S, Lundgren A

We investigate the effect of an important class of glitches occurring in the detector data on matched filter searches of gravitational waves from coalescing compact binaries in the advanced detector era. The glitches, which can be modeled as sine-Gaussians, can produce triggers with significant time delays and thus have important bearing on veto procedures as will be described in the paper. We provide approxi- mated analytical estimates of the trigger SNR and time as a function of the parameters describing the sine-Gaussian (center time, center frequency and Q-factor) and the inspiral waveform (chirp mass). We validate our analytical predictions through simple numerical simulations, performed by filtering noise- less sine-Gaussians with the inspiral matched filter and recovering the time and value of the maximum of the resulting SNR time series. Although we identify regions of the parameter space in which each approximation no longer reproduces the numerical results, the approximations complement each other and together effectively cover the whole parameter space.

New einstein@home directed search for young compact objects

Prix R

Einstein@Home is beginning a new semi-coherent search on S6 data, targeting the sky-positions of about 20 young non-pulsing neutron stars (NS) or NS candidates in supernova remnants (including Cas-A and VelaJr). These objects may be detectable if they spin within the (best) LIGO band, and are slowing down due to gravitational waves, starting from a near-breakup rotation at birth. Non-detection would therefore allow us to set constraining upper limits. The sensitivity of this search is expected to improve by about a factor of 2 on previous upper limits set on these objects. Here we present some of the design consideration that went into designing this search: What astrophysical priors do we have? What parameter space to cover? How to distribute computing power to obtain the best detection probability? How to balance these aims with the practical constraints of an Einstein@Home search?

An f-statistic based multi-detector veto for detector artifacts in continuous gravitational wave searches

Keitel D, Prix R, Papa M, Leaci P, Siddiqi M

The emission of continuous gravitational waves (CWs) is expected from spinning neutron stars with non-axisymmetric deformations. Detecting these very weak signals requires very sensitive instruments and data analysis techniques. The standard multi-detector F-statistic often used for CW data analysis is optimal in Gaussian noise, but susceptible to false alarms from noise artifacts in the form of strong monochromatic lines. In the past, ad-hoc post-processing vetoes have been used to remove these artifacts. Here we provide a systematic framework to derive a generalized form of such line vetoes (LVs). With an extended noise model including a hypothesis for single-detector lines, we can use a Bayesian odds ratio to derive a generalized detection statistic, the LV-statistic. Compared to the F-statistic, it requires very little extra computational effort. We test this LV-statistic on both simulated and real detector data from the first year of the fifth LIGO science run. We show that the LV-statistic retains most of the detection power of the F-statistic in Gaussian noise, while being much more robust in the presence of line artifacts. Furthermore, we briefly describe the advantages, in the context of Einstein@Home, of applying the LV-statistic directly on the host machines, as done in a recent search that analyzed data from the sixth LIGO science run, and whose post-processing is currently under way.

139 Avoiding selection bias in gravitational wave astronomy

Veitch J , Messenger C

Ground-based GW searches typically use a detection threshold to reduce the number of background triggers, but imposing such a threshold will also discard some real signals of low amplitude. This process can produce a selection bias in results drawn from the population of triggers unless the discarded data is properly accounted for. We will describe how selection bias can be naturally avoided by considering both the triggers and our ignorance of the sub- threshold triggers which are discarded. This approach produces unbiased estimates of population parameters even in the presence of false alarms and incomplete data.

Low latency search for gravitaitonal waves from compact binary coalesence

Wen L

For advanced gravitational-wave detectors, signals from coalescing binaries of neutron stars and stellar- mass black holes could be detected before or near their merger. I will discuss the astrophysical motivation for fast low-latency detection of such signals and present a recently developed time-domain search tech- nique aiming at extremely low latency search for gravitational waves from binary coalescence. I’ll show the result of the sensitivity our pipeline tested on simulated data as well as existing detector data and recent Engineering Run data that simulate online data from advanced gravitational-wave detectors. I’ll also present our on-going effort to improve the computational efficiency of the pipeline by using the cost-effective Graphics Processing Unit as well as a new template interpolation strategy. Implications for future joint gravitational wave and electromagnetic observations will be discussed.

Running the frequency hough all-sky continuous wave analysis on the grid: a job submission and control framework

Colla A, Astone P, D’Antonio S, Palomba C, Frasca S

In the all-sky search for continuous gravitational wave signals from unknown sources, one must apply a hierarchical approach in searching the source parameter space (source coordinates, frequency and frequency derivatives). The very high computational requirements of this search are addressed by most analysis pipelines, such as the one based on the Frequency Hough algorithm, by splitting the analysis in a series of parallel and independent tasks and running in a distributed computing environment. This translates into tens of thousands of jobs which have to be configured, submitted and monitored. We will describe the software framework we have developed to automatize the submission, monitoring, failure recovery and output retrieval of the analysis jobs within the Grid environment. We are currently applying it to the Frequency Hough all-sky search using data from the Virgo second and fourth science runs, and we will report on how the framework helps to increase the overall efficiency of the analysis.

Testing the validity of the single-spin approximation in imr waveforms

Puerrer M , Hannam M, Ajith P, Husa S

An effective single spin parameter allows us to capture the dominant spin effects in coalescences of non- precessing compact binaries, while reducing the number of physical parameters in a waveform model. To

140 leading order an optimal effective spin parameter is available in the PN regime and an inspiral model based on it has been shown to be effectual (and faithful when the masses or spins are equal). Recent phenomenological inspiral-merger-ringdown (IMR) models for black-hole binaries have used a similar parameter. We quantify how well the single spin approximation works for a set of BBH configurations with mass-ratio 4 and effective spin 0.45 in terms of parameter biases and uncertainties.

Parameter estimation improvements using a new hybrid waveform

Aoudia S, Babak S, Hinder I, Ohme F, Petiteau A, Sesana A, Wardell B

Detection of gravitational waves by a space based gravitational wave observatory such as eLISA-NGO requires not only an optimization over all the instrumental equipments but also an optimization of our knowledges about waveforms especially to improve our ability to extract information on the physical parameters of the source. Our work aims to illustrate, indeed, the importance and power of including the full waveform modeling. Especially, it reinforces a recent study which shows that by comprising all the stages of the binary merger, it is possible to reach a high level of precision measurements. For this study we build a new hybrid model, resulting from a very accurate matching between PN and NR waveforms. The matching is done for several mass ratios (q=1,2,3 and 4) by fixing spins and orbital angular momentum of the system. By the use of this new hybrid model, errors on parameters based on Fisher matrix was computed for several thousand sources by randomly choosing 7 free parameters among the 15 characterizing a coalescent binary. For the same sources the same work was repeated twice, using a pure PN model (i.e. including only the inspiral phase) : i) with 7 free parameters, ii) with 15 free parameters. The comparison of all these results enable us to compute a new law which may be used to shift or improve the precision on the measurements coming from any more realistic catalogue where the Fisher matrices were only computed using a pure PN model.

The noise characterization framework for advanced virgo detector

Cuoco E, Hemming G, Berni F, Cortese S, Colla A, Drago M, Re V, Piergiovanni F, Guidi G, Vajente G

We are approaching the era for advanced detector and we have to be ready with useful tools to help the commissioning phase.We gained experience from Virgo detector, understanding the importance of having tools to be used either for a fast noise characterization or for prompt reaction to mitigate the noise disturbances. We are working on the upgrade of the Noise Monitor Application Programming Interface (NMAPI), which gathers both in-time and on-line noise analysis pipelines. Our goal is to set up a framework in which spectral characterization is integrated with linear and non-linear noise coupling and with slow and fast non-stationarity tracking. Moreover we plan to give to the users, either data analysis or commissioning people, methods which let them use simple web interface to retrieve information from different pipelines. In this work, we describe the framework into which these tools are integrated and its upgrades, some of the pipelines already integrated and provide examples of its implementation and applications.

Calculating the significance of candidate binary coalescence signals

Dent T

In order to report detections of transient gravitational-wave signals it is necessary to obtain high sta- tistical confidence, i.e. low false alarm probability. Doing this in real data containing a population

141 of loud, unmodelled non-Gaussian transients (‘glitches’) presents several technical challenges. The es- tablished method of background estimation is to apply unphysical time-shifts to detectors at different sites, however this can be computationally expensive, requiring long stretches of data to establish high confidence, and prone to large statistical fluctuations. I will present the results of investigations into computationally efficient and reliable methods of finding the statistical significance of candidate events, including comparisons with existing methods, with a view to application on advanced detector data.

Impact of noise cancellation on the search for gravitational wave transient signals.

Re V , Drago M, Klimenko S, Mazzolo G, Necula V, Prodi G, Salemi F, Tiwari V, Vedovato G, Yakushin I

One of the prominent problems in the search for gravitational waves (GW) is the presence of non gaussian excess noise which may hide a GW signal due to increased false alarm rate. Regression analysis of auxiliary environmental and instrumental channels can provide a partial noise cancellation by measuring the linear (or non linear) coupling of the auxiliary channels to the GW channel and thus subtracting such predicted contributions from the noise. In this work we explore the impact that this method has on the search for transient GW signals. We present preliminary results of the application of noise cancellation on a set of real data from the first joint LIGO-Virgo run. The efficiency of the method and the impact on the search sensitivity is tested by means of software injections simulating transient signals in the data at different frequency bands. Investigations are being pursued in particular within the lower frequency band (20-200 Hz) which will be of particular astrophysical interest in future observations of the Advanced Detectors Era, being crucial for the achievable range of BH-BH coalescences.

Searching for a stochastic gw background from populations of neutron stars in the data from the ligo & virgo detectors

Bose S, for the LIGO-Virgo Collaboration .

We describe a search in the LIGO and Virgo data for a stochastic gravitational-wave background from populations of rotating non-axisymmetric neutron stars in our galaxy and in the Virgo cluster. Employing multi-baseline radiometry bounds on the GW strain power from these populations can be obtained, which, in turn, can constrain neutron star equations of state. The current status of the search will be presented. We also assess the expected performance of this search using forthcoming second-generation detectors, including the improvement from locating one of the Advanced LIGO detectors in India.

Generic black-hole-binary waveform models: issues and progress

Hannam M , Schmidt P, Ajith P, Bohe A, Husa S, Ohme F, Puerrer M

Current phenomenological waveform models for the inspiral, merger and ringdown of non-precessing black-hole binaries make use of a single spin parameter, which is an appropriately weighted sum of the two black-hole spins. The errors incurred in making this approximation in GW searches and parameter estimation are in most cases smaller than the errors due to waveform degeneracies between the binary’s mass ratio and the black-hole spins. In generic (precessing) binaries, additional approximate degeneracies, plus the recent insight that inspiral and precession effects can be effectively decoupled, open the possibility of constructing simple generic waveform models. We present progress in constructing such models.

142 Approximation methods for bayesian detection statistics in a targeted search for continuous gravitatonal waves

Whelan J , Prix R

Prix and Krishnan [CQG 26, 204013 (2009)] showed that the standard maximum-likelihood statistic used in continuous gravitational-wave searches, known as the F-statistic, could also be interpreted as a Bayes factor using an unphysical prior distribution on the amplitude parameter space. They defined an alternative statistic using physical priors on the amplitude parameters, particularly the geometrical parameters of neutron star inclination and polarization angles, known as the B-statistic, and showed it to be more powerful in the case where the unknown amplitude parameters are drawn from the physical prior distribution. Marginalizing over the amplitude parameters requires a multi-dimensional integral which must in general be done numerically. We describe approximation methods which allow analytic evaluation of this integral, allowing the more powerful search to be done without a large increase in computational resources.

Impact of noise cancellation on the search for gravitational wave transient signals.

Re V , Drago M, Klimenko S, Prodi G, Vedovato G, Tiwari V, Necula V, Mazzolo G, Salemi F, Yakushin I

One of the prominent problems in the search for gravitational waves (GW) is the presence of non gaussian excess noise which may hide a GW signal due to increased false alarm rate. Regression analysis of auxiliary environmental and instrumental channels can provide a partial noise cancellation by measuring the linear (or non linear) coupling of the auxiliary channels to the GW channel and thus subtracting such predicted contributions from the noise. In this work we explore the impact that this method has on the search for transient GW signals. We present preliminary results of the application of noise cancellation on a set of real data from the first joint LIGO-Virgo run. The efficiency of the method and the impact on the search sensitivity is tested by means of software injections simulating transient signals in the data at different frequency bands. Investigations are being pursued in particular within the lower frequency band (20-200 Hz) which will be of particular astrophysical interest in future observations of the Advanced Detectors Era, being crucial for the achievable range of BH-BH coalescences.

A model-based cross-correlation search for gravitational waves from scorpius x-1

Whelan J , Sundaresan S, Peiris P

The low-mass X-ray binary (LMXB) Scorpius X-1 (Sco X-1) is a promising source of gravitational waves in the advanced detector era. A variety of methods have been used or proposed to perform the directed search for gravitational waves from a binary source in a known sky location with unknown frequency and residual uncertainty in binary orbital parameters. These include a fully coherent search over a short observation time, a search for an unmodelled narrowband stochastic signal, and a search for a pattern of sidebands arising from the Doppler modulation of the signal by the binary orbit. A modification of the cross-correlation method used in the stochastic-background search has been proposed, which takes into account the signal model of a rotating neutron star to allow cross-correlation of data from different times. By varying the maximum allowed time lag between cross-correlated segments, one can tune this semicoherent search and strike a balance between sensitivity and computing cost. We describe the

143 details of and prospects for application of this method to searches for Sco X-1 and other LMXBs. We also present some recent enhancements to the Cross-Correlation search method.

Construction and validation of multi-mode hybrids obtained from gluing post-newtonian and numerical relativity waveforms

Calderon Bustillo J

The construction and accuracy of hybrid post-Newtonian/numerical relativity waveforms of the dominant l=—m—=2 spherical harmonic modes has been studied in the past with considerable detail. In this work we generalize to non-dominant modes and study impact and the errors of the procedure from a data- analysis point of view.

Sensitivity of coincident and coherent cbc searches at finite computing cost

Dal Canton T , Keppel D

Searches for gravitational radiation from coalescing compact binaries use single-detector matched filters followed by a coincidence stage. An alternative method is the so-called coherent matched filter, where data from all interferometers are combined coherently into a single detection statistic, automatically taking into account the different responses and time delays of the instruments. This method is expected to be more sensitive but also computationally more expensive and has never been used in a blind all- sky CBC search. Important open questions for the advanced detector era are i) at what computing cost the coherent method becomes more sensitive and ii) whether an interesting sensitivity increase can be achieved at a lower cost by combining the two methods into a “hierarchical” search. We address these issues by estimating the sensitivity and computing cost of the coincident, coherent and hierarchical methods under the main assumption of stationary Gaussian noise. We compare the sensitivities at fixed computing cost for different configurations of advanced detectors, including the projected evolution of advanced sensitivity curves.

Stochastic background of gravitational waves generated by compact binary systems

Evangelista E

Soon after the publication of the General Theory of Relativity in its definitive form in 1916, it was noticed that some of its solutions depicted gravitational waves, that is, perturbations in the spacetime which propagate at speed of light and that could in principle be detected. According to such solutions, any mass distributions that underwent some kind of time variation would become a source of gravitational radiation, since at a given moment the spherical simmetry were broken. Thus, from the astrophysical viewpoint, virtually all the processes involving mass deformations and movements, such as stars and black holes, could be considered as a potential source of gravitational waves. Particularly, we are dealing with cosmological compact binary systems in circular and eccentric orbits and the spectra generated by the population of those sources. The main purpose of our work is the formulation of a new method of calculating the spectra generated by such a population during the periodic and quasi-periodic regimes. We used an analogy to a problem of Statistical Mechanics in order to establish the fundamentals of such a method, besides taking into account the time variation of the orbital parameters such as eccentricities and frequencies.

144 C3 - Progress and Challenges in Advanced Ground Based Detectors

Oral session

Advanced ligo installation lessons and prospects

Bransotti L

Installation of the Advanced LIGO detectors is nearing completion with full interferometer commissioning expected to begin in the next year. The installation has proceeded on different tracks at the Hanford, Washington and Livingston, Louisiana sites. This has enabled us to get early experience with locking a single arm (Hanford) and with commissioning the Input Mode Cleaner (Livingston). The experience gained from installation of these complex instruments with emphasis to lessons learned, pitfalls and success stories may inform our approach to future upgrades and be of benefit to those who may attempt similar endeavours in the near future. The talk will cover the installation process with special attention to these issues.

Towards advanced virgo

Losurdo G

The Virgo interferometer is currently being upgraded to a second generation detector, Advanced Virgo. In this talk we discuss the status and plans of the Advanced Virgo project in the framework of the international effort to create a network of second generation interferometers, aiming to open the way to gravitational wave astronomy. Looking back at the recent experience with the commissioning of Virgo we discuss the most likely challenges to be faced to approach the detector design sensitivity.

Progress and challenges of kagra

Kawamura S

KAGRA is the only detector that employs cryogenic mirrors and underground facilities among the 2nd- generation detectors. Since we have been excavating the tunnel and developing the various technologies related to the cryogenic mirrors, I will present ”lessens learned”, which would be useful for the develop- ment of the 3rd-generation detectors, such as ET. In this talk I will also mention challenges and difficulties

145 we have encountered in the design and prototype-test phase of KAGRA. The objectives, design details, and schedule of KAGRA will be also presented.

New in-air seismic attenuation system for the next generation gravitational wave detector

Blom M , Bertolini A, van den Brand J, Beker M, Bulten H, Rabeling D, Hennes E

During the combined commissioning and science run of the Virgo gravitational wave detector in 2010, an extensive noise study revealed that some of the injection/detection optics on the external injection bench (EIB) made a significant contribution to the Virgo noise budget. Resonances of the EIB where excited by seismic ground motion and introduced a significant amount of beam jitter between 10 and 100 Hz and between 200 and 300 Hz. This beam jitter would limit the sensitivity of Advanced Virgo and needs to be reduced to allow the detector to reach its full potential. Therefore, new support structures that will isolate the EIB from seismic ground motion in six degrees of freedom and operates in air, has been constructed and tested at Nikhef. The system uses passive mechanical filters (inverted pendulums and geometric anti-spring filters) and feedback to obtain the desired level of isolation. It was installed and commissioned between November 2011 and March 2012, kicking off the upgrade towards Advanced Virgo. We will give an overview of the system and show the performance we have achieved.

Monolithic suspensions for advanced gravitational wave detectors and quantum radiation pressure experiments

Hammond G

The worldwide network of Gravitational Wave detectors are currently undergoing sensitivity upgrades which will open the gravitational window on the Universe. The Advanced LIGO (aLIGO) detector utilises fused silica monolithic suspension to lower suspension thermal noise and increase the operating bandwidth down to 10Hz. The suspension utilises four fibres of 400 micron diameter to suspend the 40kg optic and is a major deliverable from the Glasgow group. This talk will provide an overview of fused silica as a material for the construction of gravitational wave detector suspensions operating at room temperature. The fabrication of suspension elements, strength testing and the performance of the aLIGO suspension, in addition to the potential for future upgrades will be detailed. The talk will also focus on the use of crystalline silicon as a material for cryogenic upgrades to aLIGO or future detectors such as the Einstein Telescope. The talk will further motivate the use of thin fused silica fibres (with diameter less than 20 microns) to suspend 100g test masses for quantum radiation pressure experiments such as the 10m prototype at the Albert Einstein Institute in Hannover. First results from a triple stage prototype suspension, which features a fused silica monolithic final stage, will be detailed and compared with a theoretical analysis.

Development of the coatings for the advanced ligo and advanced virgo mirrors

Flaminio R

LMA is realizing the coatings for the mirrors of Advanced LIGO and Advanced Virgo. The most critical requirements for these coatings are the optical absorption, the mechanical losses and the coating uniformity required to attain final mirror flatness specifications. First we will present the techniques

146 developed to improve the coating uniformity and the results obtained on the first Advanced LIGO mirrors. The mechanical losses and optical absorption measured on the multilayer coatings will be presented as well. In particular the measurement of the mechanical losses for different kind of multi-layers will be shown.

Progress on the cryogenic system for the interferometric cryogenic gravitational wave telescope, kagra, - design, fabric

Kimura N , Sakakibara Y, Suzuki T, Yamamoto K, Dan C, Tokoku C, Kume T, Koike S, Ohashi M, Kuroda K, Naticchioni L, Majorana E

Japanese large-scale cryogenic gravitational wave telescope, KAGRA, aims to detect gravitational waves using an interferometer having 3 km in length of arms. The notable feature of KAGRA is four main mirrors of the interferometer are cooled down below 20 K in order to reduce thermal noise. With the design of the cryogenic system for KAGRA, a cryo-payload consisting of the mirror and its suspension system is connected with two very-low-vibration cryo-cooler units as cooling devices, and is surrounded by the radiation shield (2.5m3 in volume) below 20K in a cryostat. Each cooling device consists of a pulse-tube type cryocooler (0.9W at 4K), a specifically designed mechanical frame and the conduction cooling links made of 6N class high purity aluminum. Fabrication of four cryostats and sixteen very- low-vibration cryocooler units was started at 2011, and completed on the end of March 2013. All of the cryocooler units confirmed their expected cooling performance, as 2.5 W at 9 K, and the overall vibration characteristic less than 10−7m/Hz0.5at the connection edge of conductive cooling passage. KAGRA collaborators carried out total performance tests including cooling characteristic with a half size of dummy cryo-payload and measurements of vibration of the radiation shield. Detail of thermal and mechanical design of the cryogenic system for KAGRA and its performance will be reported in the conference.

Stabilized high power lasers for second and third generation gravitational wave detectors

Willke B, Bogan C, Carbone L, Damjanic M, Feldbaum D, Frede M, Freise A, King P, Kwee P, Meier T, Oppermann P, Poeld J, Puncken O, Savage R, Theeg T, Wessels P, Winkelmann L

We present the design and performance of the pre-stabilized 200W high power laser (PSL) of the Ad- vanced LIGO Gravitational Wave Detector (AdvLIGO) and some laser developments relevant for Third Generation Gravitational Wave Detector (TG-GWDs). Three of the AdvLIGO PSLs are installed and in operation since up to three years. All systems were fully characterized and their performance will be described by a collection of noise spectra and long term data. One of these PSLs was used to generate a 135W laser beam at a wavelength of 532nm and a laser beam in the higher spatial Laguerre LG33 mode with 83W. This PSL was furthermore used to demonstrate a relative power noise sensing sensitivity of 1x10E-10 1/sqrt(Hz) and to measure thermal lensing in several optical materials. In the near future we will characterize and stabilizes a 200W fiber amplifier. The design of this laser and first characterization results will be presented.

147 Characterization of the input optics for the advanced ligo detectors

Mueller C , Mueller G, Tanner D, Martin R, Feldbaum D, Ciani G, Fulda P, Heintze M, Frolov V, Derosa R, Effler A, Poeld J, Korth W

Over the last several decades a network of ground based interferometric gravitational wave detectors was successfully designed, built, and operated at sensitivities necessary for the detection of gravitational radiation. During the operation of this first generation of gravitational antennae a worldwide research effort led to the design of upgrades to this network of detectors which promises increased sensitivity by a factor of 10 across the sensitive band. At the Laser Interferometer Gravitational-Wave (LIGO) obser- vatories in the United States many of the upgraded systems have been installed, and the commissioning and integration phase has begun. This talk will focus specifically on the input optics of the Advanced LIGO detectors. The input optics are tasked with stabilizing and preparing the laser beam before being injected into the interferometer. In particular, a set of low noise, deep modulation depth RF sidebands must be added to the beam; the frequency of the laser must be stabilized to the level of 1 × 10( − 3)Hz/rtHz at 100Hz; and a Faraday Isolator at the output of the input optics must provide 30 dB of isolation from the interferometer reflected light. All of this must happen while operating at CW powers of 150 W and maintaining a 75 % throughput efficiency. This talk will describe how the input optics have been designed to meet these stringent requirements and present a set of measurements showing how well it has succeeded.

The arm length stabilization system for advanced ligo lock acquisition

Mullavey A, Slagmolen B, Izumi K, Sigg D, Evans M, Barsotti L, Kawabe K, Dwyer S, Miller J, Shaddock D, McClelland D, Fritschel P

The Laser Interferometric Gravitational-Wave Observatory (LIGO) is currently being upgraded to a dual- recycled Fabry-Perot Michelson interferometer. This upgraded interferometer, referred to as Advanced LIGO, will be an order of magnitude more sensitive over the gravitational wave detection band than Initial LIGO. This increase in sensitivity comes at the cost of added complexity to the interferometer. To reach design sensitivity, the interferometer’s five length degrees of freedom need to be held at their operating points by feedback control systems. However, initially the interferometer lengths are in a state of flux, and the act of bringing the interferometer into a controlled state is a non-trivial task due to a couplings between the cavities, the narrow linear range of the length readouts, and weak actuators. This process of bringing the interferometer into a controlled state is called lock acquisition. To reduce the complexity of the Advanced LIGO lock acquisition scheme, an Arm Length Stabilization (ALS) system has been developed. This ALS system will employ auxiliary frequency doubled Nd- YAG lasers to sense the lengths of the fabry-perot cavities in the arms independent of the rest of the interferometer. This ALS readout will be used to suppress the residual arm motions to less than 1nm rms, and also detune the arm cavities off resonance with the primary science laser, so that the central degrees of freedom can be locked.

Commissioning geo-hf: integrating permanently a squeezed vacuum source and increasing the laser power

Dooley K

The German-British laser interferometer gravitational-wave detector, GEO600, located near Hannover, Germany has served as the sole gravitational-wave detector in operation since September 2011. In

148 parallel to its data-taking mode, GEO600 is in the midst of implementing a series of upgrades intended to improve its strain sensitivity at high frequencies (above 500 Hz). Called GEO-HF, this programme involves a combination of demonstrating advanced detector technology such as a permanent application of squeezing, and developing solutions to the technical challenges of increasing the circulating laser power from about 2 kW to 20 kW. We present the latest commissioning progress including results in finding the best phase and alignment signals to actively control the squeezed vacuum field with respect to the interferometer, developments in the design and use of a thermal compensation system to improve the interferometer’s output beam mode quality, and research into new schemes for automatically aligning the output field to an output mode cleaner.

Quantum noise reduction using squeezed states in ligo

Barsotti L, Dwyer S

A world-wide network of laser interferometric detectors is seeking the first direct observation of gravita- tional waves. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometer level sensitivity of the Michelson interferometers deployed for this task. The technique of injecting squeezed states of vacuum into an interferometer to improve the shot noise limit was proposed over 30 years ago, and it has been recently adopted to improve the sensitivity of the GEO600 detec- tor. In this talk we show how injection of squeezed states of vacuum improved the performance of the H1 detector of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the standard quantum limit, demonstrating the best broadband sensitivity to gravitational waves ever achieved.

Towards the quantum limit: update from the aei 10-meter prototype

Fricke T , for the AEI 10m Prototype team

Future gravitational wave detectors will be limited in sensitivity by quantum radiation pressure noise and quantum shot noise. At the AEI 10-meter prototype facility we are building a Fabry-Perot Michelson interferometer designed to meet the Standard Quantum Limit (SQL) at 200 Hz, allowing investigation into techniques to surpass this limit. One technical challenge is the use of marginally stable optical cavities. I will describe the current status, recent progress, and near-term plans of the 10-meter project, including our chosen initial configuration that will allow us to gain early experience with marginally stable cavities.

149 Poster session

Thermo-acoustic radiation pressure noise in gravitational wave detectors due to three mode interactions

Ju L, Zhao C, Blair D

Triply resonant three mode interactions in long optical cavities have been shown to lead to enhanced scattering of carrier light from the ultrasonic acoustic modes of the test mass mirrors. At high optical power, this can lead to parametric gain R¿1 for a few acoustic modes with strong spectral and spatial overlap. Numerous ( 103 ) acoustic modes of the test masses are predicted to have R¿10-3. Experimental studies have shown that such modes also strongly scatter the carrier light, enabling very sensitive readout of the acoustic modes. We show here that 3-mode scattering from the large population of ultrasonic modes causes random changes in occupation number of the carrier light. Because the thermal fluctuation time scale (set by the acoustic mode relaxation times) is typically a few seconds, the carrier light is scattered into cavity transverse optical modes with a randomly fluctuating amplitude, on the same time scale. This creates a source of radiation pressure noise at low frequency. The noise amplitude can be reduced by cryogenic cooling and reduced in peak frequency by using lower acoustic loss test masses. Passive damping techniques, proposed for reduction of the risk of parametric instability, also act to increase the peak frequency of thermo-acoustic radiation pressure noise. We will compare the magnitude of such noise with quantum noise in gravitational wave detectors.

Early detection of parametric instability

Blair C , Susmithian S, Zhao C, Qi F

Advanced gravitational wave detectors will soon be running with stored optical power sufficient to result in possible three mode parametric instabilities. Instabilities occur through the time varying radiation pressure force generated by the beating of two optical modes, a high power fundamental mode and a higher order mode created by test mass acoustic mode scattering. This radiation pressure force acts to further excite test mass acoustic modes. In this presentation methods are introduced for predicting instabilities well before they occur in advanced gravitational wave detectors, by injecting high order optical modes which have substantial spatial overlap with the test mass acoustic modes. Early or low power prediction of parametric instability will allow us to pre-empt stability issues, activate suppression mechanisms and keep a quiet cavity while the optical power in the detectors is increased. Methods presented use relatively low optical power and limited additional infrastructure. Techniques for the suppression of parametric instability are reviewed. The preliminary experimental results demonstrated at the Gingin 80m high power facility will be presented.

Mode healing in advanced ligo

Bond C

As Advanced LIGO, and other advanced detectors, enter the commissioning phase it is crucial to under- stand the expected behaviour of the interferometers in the presence of deviations from the ideal design parameters. An important part of the commissioning process is the characterisation of such deviations, including those that affect the shape of the beam, such as the deviation of the mirror surfaces from

150 an ideal sphere. Two major differences between LIGO and Advanced LIGO, the presence of a signal recycling mirror and stable recycling cavities, will have a strong effect on beam shape distortions and the dark fringe contrast. In GEO 600 the use of signal recycling reduces the light scattered into higher-order modes, the so-called ‘mode-healing’ effect. Here we present an analysis of this effect for the Advanced LIGO configuration. We discuss this in the context of distortions in the two arm cavities, as well as the impact of the tuning and reflectivity of the signal recycling mirror.

Mode matching and astigmatism requirements for the use of high-order laguerre-gauss mode beams in advanced detectors

Sorazu B

Next generation ground based interferometric gravitation wave (GW) detectors (or advanced detectors) are expected to be limited at peak sensitivity by coating thermal noise in the test-mass mirrors of the interferometer. The use of light beams with an intensity profile more homogeneously distributed than the fundamental Gaussian mode shape has been suggested to reduce this thermal noise. Higher-order Laguerre-Gauss beams are one of such beams with the added advantage of compatibility with normal spherical mirrors currently used in GW detectors. We have found that high-order Laguerre-Gauss mode beams are more susceptible to astigmatism and mode mismatch than a fundamental Gaussian mode beam. Here we report on the requirements on both mode matching and mirror astigmatism for advanced detector.

Results from raman spectroscopy and direct thermal noise measurements on tantala and silica.

Granata M

Tantala and silica are the two amorphous materials that are used in optical coatings for the advanced detectors and possibly in the future high-frequency ET detector. Structural relaxations inside these two materials are believed to be responsible of the thermal noise level affecting the optical coatings. In the frequency band where the GW detectors are most sensitive, thermal noise from coatings is the limiting factor for the detector performance. In order to detect the mechanisms that are responsible of the structural relaxation LMA has started a collaboration with the Institute Lumiere Matiere in Lyon to investigate the Raman spectra of tantala and silica. Results on this analysis correlated with results from mechanical loss measurements, varying annealing temperature and stress level, will be presented. Finally, a novel interferometric system, developed by the Ecole´ Normale Sup´erieurein Lyon, able to measure thermal noise at low frequency will be shown and the first results discussed.

State observation and miso control for in-vacuum suspended optical benches in advanced virgo

Beker M , van den Brand J, Bulten H, Bertolini A

Scattered light and control noise issues in Advanced Virgo necessitate the use of vibration isolation systems to suspend in-vacuum optical benches. Five of these benches will be suspended by MultiSAS: a compact multi-stage hybrid isolation system. To achieve the target residual motion of the optical benches, feedback control is implemented to actively damp the system’s resonance frequencies. The design and characterization of the MultiSAS prototype will be addressed. In addition, a novel approach

151 to the control of the vertical degree of freedom, utilizing a Kalman state observer and a linear quadratic regulator, is adopted to optimize a multiple-in single-out feedback controller.

Electro-optic modulators and power control for advanced ligo

Tanner D, Feldbaum D, Gleason J, Heintze M, Martin R, Mueller C, Mueller G, Quetschke V, Reitze D, Tellez G, Williams L

The Input Optics (IO) of advanced LIGO includes custom-designed electro-optic modulators and laser power control. These are described in this contribution. The phase modulators have 3 sets of RF electrodes in order to provide three modulation frequencies using a single RTP crystal. The crystal is slightly wedged to refract the wrong polarization by different angles than the desired one, sending the wrong one to a baffle and thereby reducing RF amplitude noise. The power control uses two thin-film polarizers, a water-cooled beam dump, and motorized half-wave plate allowing automated control of the laser power delivered to the input mode cleaner. The performance of these devices will be described. This research has been supported by the NSF through grants PHY-0855313 and PHY-1205512.

Characterization of the lasy-50 co2 laser to be used in the advanced virgo tcs

Cesarini E, Coccia E, Cortese M, Fafone V, Lorenzini M, Malvezzi V, Minenkov Y, Mudadu L, Rocchi A

In 2nd generation GW interferometric detectors axisymmetric aberrations in the recycling cavities need to be compensated. The correction of optical aberrations will be provided through CO2 projectors, because the light at 10.6 um is completely absorbed by the optics. The Thermal Compensation System (TCS) strategy is to use a Double Axicon System (DAS). Optical simulations have shown that the heating profile generated by a single axicon is not the optimal one for the correction of axisymmetric defects, so the solution chosen for AdV TCS CO2 projector is based on known technology and allows to approximate the optimized heating pattern by combining the action of two axicon-generated heating patterns. The laser selected for the AdV TCS CO2 projector is the LASY-50 from Access Laser Company, capable of delivering up to 50 W. This laser has an internal system for power stabilization: the length of the RF cavity is actively controlled with a piezo actuator. A detailed study of the intensity noise of the laser has been performed to understand the behavior of the laser itself and its power control system, in relation with environmental parameters, such as temperature, acoustic and mechanical noise. An intensity stabilization system, made of an AOM and 2 photodiodes, to make the noise compliant with the AdV sensitivity has been included. Moreover an investigation of its optical parameters, gaussianity, astigmatism, polarization extinctioncoefficient and jittering will be presented.

152 Thermal compensation system for non symmetric optical distortions in future gravitational wave detectors

Lorenzini M , Cesarini E, Coccia E, Cortese M, Fafone V, Malvezzi V, Mudadu L, Minenkov Y, Rocchi A

In second generation gravitational wave interferometric detectors, optical aberrations in the recycling cavities have both an axisymmetric and a non symmetric contribution. The Thermal Compensation System (TCS) strategy to compensate for these aberrations is to use a Double Axicon System (DAS) for the symmetric part and a Scanning System (SS) for residual distortions. The SS designed for Advanced Virgo is conceived to project onto the test masses a heating pattern suitable to correct locally for the non symmetric optical path distortions. The latter is achieved by scanning the central area with a CO2 laser spot with adjustable intensity. Several heating pattern reproduction methods and scanning schemes have been proposed and tested and results will be reported. Alternative solutions are under investigation in view of application in future GW detectors. Of particular interest are those methods capable of shaping a single CO2 beam to meet the requested heating pattern, avoiding the spot to be drawn across the optics central area, therefore resulting in a DC system. This solution allows to get rid of the noise due to the scanning frequency. Optical simulations have been carried out to study the efficiency and dynamics of these static devices in comparison with minimum distortion requirements.

Automatic alignment for the geo600 squeezed light application

Schreiber E

The GEO600 gravitational wave detector continues to successfully use a squeezed light source to improve the detection sensitivity beyond the limits set by quantum shot noise. One important aspect of achieving the best possible squeezing performance is a good alignment of the squeezed vacuum field to the carrier beam at the output of the Michelson interferometer. To ensure optimal alignment on long time scales and in the presence of suspended optics an automatic alignment scheme was implemented. We compared different alignment signals and investigated techniques to automatically tune the system for best resulting sensitivity. Our contribution will present the design and status of this first squeezed light automatic alignment system in a gravitational wave detector.

Impact of detector characterization on geo600 commissioning

Leong J

A few years ago the GEO600 commissioning team took up the task of leading a small group working on detector characterization (GEO-DC) focused on aiding the commissioning process. This endeavor has been a very positive experience. I will discuss here the structure of the GEO-DC group, including the roles that various members played, which was important to the creation of tools for commissioning. Next some highlights of these contributions will be presented. The discussion will conclude with describing a spectrogram-like data plotting method which will from now on be an indispensable tool for the GEO600 commissioning process. The path we took to create this tool is the perfect example of what we initially set out to do, which was to utilize a very strong interaction between a broad spectrum of people from commissioning to data analysis.

153 Acoustic mode damper for parametric instabilities control

Gras S, Evans M, Fritschel P

A long standing concern for advanced gravitational wave detectors have been parametric instabilities. These instabilities may arise as optical energy stored in the interferometer leaks into mechanical modes of the test-masses, which can lead to run-away energy transfer. Should instabilities occur, they will limit the power that can be use in the new detectors. The research presented here focuses on the design and construction of piezoelectric resonant dampers for suppressing unstable ultrasonic acoustic modes while avoiding increased thermal noise. These dampers are designed to be easily retrofitted to the current Advanced LIGO test-masses.

Characterization of the mirror internal losses of the suspended test masses by means of an interferometric sensor: res

Puppo P

We have developed an interferometric sensor to characterize the internal losses of suspended mirrors. This system, installed in the Virgo Rome laboratory, has a sensitivity of 10−14m/sqrt(Hz) in the kHz range and was used to measure the internal losses of the Virgo+ test masses dismounted from the detector. The results were compared with the Q’s measured during the Virgo+ data taking. The system can be used to measure the mechanical losses of the test masses in Advanced Virgo before installing them in the detector.

Beam shutter for kagra

Ueda S, Westphal T, Somiya K

In high power laser interferometers, for example KAGRA and LIGO, a sudden high power beam that occasionally enters a sensitive photo-detector due to accidental misalignment of optical components can destroy the photo-detector. To protect the photo-detector from breakdown, a mechanical beam shutter, which interrupts the beam line immediately after the onslaught of the beam to the photo-detector, are necessary. In our poster, we show how to make the beam shutter system from a rotary voice-coil motor of a computer hard disk drive and a current drive circuit LMD18200, which ensures the required closing speed 1ms (1ms is the temporal requirement in KAGRA), and also show how to measure the shutter closing speed.

A solution of an offset problem in detuned rse

Saito N , Friedrich D, Aso Y, Somiya K

We have demonstrated our method to cancel the offset using the mixed modulation in a simple experiment with a single cavity. While our goal for the gravitational-wave detector is to cancel the offset due to the detuning of the signal recycling cavity on other degrees of freedom, the fundamental concept is to optically create the offset using amplitude modulation sidebands. The purpose of our experiment here is to demonstrate the creation of the offset on the control signal in a single cavity by mixing the amplitude modulation in the phase modulation.

154 The aei 10m prototype interferometer frequency control using a reference cavity

Kawazoe F

The AEI 10m prototype project will soon be providing a test bed for very sensitive interferometric experiments, such as a sub-SQL interferometer, which will be utilized to test new techniques to reach the Standard Quantum Limit and even go beyond it. The experience and knowledge gained form this experiment can be applied to large-scale interferometric gravitational detectors to improve their sensi- tivities. In order for the sub-SQL interferometer to achieve the required sensitivity to surpass the SQL, all possible noise sources need to be suppressed sufficiently including laser frequency noise. The AEI 10m prototype will use an NPRO 2W Nd:YAG laser whose frequency must be stabilized to a level of 10 − 4Hz/sqrtHz at 20Hz rolling off to below 6 × 10 − 6Hz/sqrtHz above 1kHz. This includes the safety margin of 10. In order to stabilize the frequency noise to this level, a 20m optical path length triangular suspended cavity called the reference cavity will be used. It is expected that tight length control as well as angular control of the reference cavity’s mirrors is necessary to reach this stringent requirement.

Design of a glass optical parametric oscillator to produce audio frequency squeezing for gravitational wave detection

Mansell G, Wade A, Chua S, Slagmolen B, Shaddock D, McClelland D

The next generation of interferometric gravitational-wave detectors are expected to be broadly limited by quantum noise. It has been shown that injection of squeezed states of light into these detectors can increase their sensitivity. For future detectors a squeezed light source must operate at low frequencies, be vacuum compatible and produce squeezing over long time scales. The design of a glass optical parametric oscillator (OPO) cavity, which is expected to produce greater than 10 dB squeezing in the audio frequency band, is presented here. The glass-based design is cho- sen for its long term stability and vacuum compatibility. The cavity will be in a bow-tie configuration for backscatter resistance, and doubly resonant at the 532 nm pump and 1064 nm fundamental wave- lengths. Components will be mounted on a glass slab base using the optical contacting technique. Design challenges such as the mounting of the non-linear crystal, alignment tolerances, phase matching and temperature control will be addressed.

Adaptive thermal lenses for gravitational wave detectors

Fulda P, Arain M, Williams L, Liu Z, Mueller G, Reitze D, Tanner D

In the high-laser power advanced gravitational-wave detector era, optimizing and maintaining the mode matching between the optical cavities in the presence of thermal lensing of the optics and static mode mismatches is required to maintain optimal detector performance at all power levels. I will discuss an adaptive thermal lensing device designed and characterized at the University of Florida for the purposes of optimizing the mode matching within the Advanced LIGO detector. I will present the results of the first measurements of the dynamic range of the device operated in vacuum, as well as measurements of the impact of using the device on beam quality. I will also show the use of the device to correct for astigmatism in laser beams.

155 The measurement of the vibration in the radiation shield of kagra

Chen D, Yamamoto K, Suzuki T, Kimura N, Koike S, Kume T, Tokoku C, Sakakibara Y, Naticchioni L, Majorana E, Kawamura S

The Large-scale Cryogenic Gravitational Wave Telescope named KAGRA is under construction in the Kamioka mine. In the final stage the mirrors forming the arm cavities of this Dual-recycled Fabry-Perot Michelson Interferometer will be cooled down to 20K in order to decrease the thermal noise. The main mirrors of KAGRA are suspended in a cryogenic payload which is surrounded by the radiation shields. The payload is connected with cryocoolers and radiation shield by heat links made of pure aluminum. The vibration of the radiation shield can be a noise source for gravitational wave detection. At first, the heat links can transmit the vibration of the radiation shield. Moreover, the scattered light reflected by the vibrating radiation shield can contaminate the output of the detector when this light recouples into the main laser. So it is important to measure the vibration in the radiation shield for KAGRA and the future cryogenic interferometer gravitational wave detectors. In order to measure the vibration of the radiation shield, we developed an accelerometer which operates in cryogenic temperature and vacuum. We installed the accelerometer in a radiation shield of KAGRA in a manufacturing plant. We measured the spectrum of the vibration during the cooling time. We also compared this result with the vibration of outside of the cryostat and our simulation result. We will report the development of the cryogenic accelerometer and the measurement result.

Design study of the kagra omc

Kumeta A, Yano K, Friedrich D, Gossler S, Somiya K

KAGRA is a Japanese large-scale cryogenic gravitational-wave detector currently under construction in Kamioka Mine. The sensitivity of KAGRA is mainly limited by quantum noise. In order to reduce the quantum noise level, KAGRA employs an OMC at the signal extraction port and uses the DC readout technique. The proper design of the OMC is a key element to realize the target sensitivity of KAGRA. We have built a prototype interferometer for the OMC experiment. The aim of the prototype experiment is to develop a suitable alignment sensing scheme that will be adopted to KAGRA. It is also important to select a proper g-factor of the OMC cavity so that most of the spatial higher order modes leaking out from the main interferometer can be filtered out. We have performed numerical simulations of the higher order modes for KAGRA using the simulation code FINESSE based on the modal expansion.

Impact of backscattered-light in squeezing-enhanced ligo

Chua S, Dwyer S, Barsotti L, Sigg D, Schofield R, Frolov V, Kawabe K, Evans M, Meadors G, Factourovich M, Gustafson R, Smith-Lefebvre N, Vorvick C, Landry M, Khalaidovski A, Stefszky M, Mow-Lowry C, Buchler B, Shaddock D, Lam P, Schnabel R, Mavalvala N, McClelland D

Squeezed states of light have been recently used to improve the sensitivity of laser interferometric gravi- tational wave detectors beyond the quantum limit. To establish quantum engineering as a realistic option for the next generation of detectors, it is crucial to study and quantify the noise coupling mechanisms which injection of squeezed states could potentially introduce. We present a direct measurement of the impact of backscattered-light from a squeezed-light source on one of the 4 km long detectors of the Laser Interferometric Gravitational Wave Observatory (LIGO). The backscattered-light power reaching the interferometer readout photo detector was determined to be 260 fW, and the background backscatter noise level was at least a factor of 5 below the interferometer quantum noise in the 50 Hz to 300 Hz detection region. We also show how our measurements compare

156 to backscattering requirements for advanced detectors currently under construction, such as Advanced LIGO, and how it informs the design of compatible squeezed light sources.

A new setup for torsion-bar antenna

Shoda A, Ando M, Aso Y, Ishidoshiro K, Tsubono K

At frequencies around 1.0 Hz, many interesting targets for gravitational wave (GW) detectors is expected to be observed, such as GWs from intermediate mass black hole binaries, a stochastic GW background, and so on. However, neither ground based interferometers, Pulsar timing, nor Doppler tracking method has a good sensitivity to them. Space GW antennas will have good sensitivities at frequencies lower than 1 Hz but they costs a lot of money and time. Then, we have proposed a new detector, Torsion- bar Antenna (TOBA). TOBA is composed of two bar-shaped test masses, which rotate differentially according to the tidal force caused by GWs. TOBA fundamentally has a good sensitivity around 0.1 - 1.0 Hz even on the ground because the low resonant frequency in the rotational degree of freedom suppresses the seismic noise. And TOBA needs only 10 m scaled experimental setup in order to obtain the sensitivity of 10−19 in strain at 1 Hz. Merits in TOBA is simple, small, and inexpensive. We have already developed the first prototype TOBA and performed an observational run. As a result, we have set the first upper limit on a stochastic GW background at 0.04 − 0.8Hz. Now, we are proceeding to the next step. The key techniques in our new setup are a vibration isolation system and a cryogenic system. Also, we are planning to perform a new observation method which will enhance its viewing angle. We will introduce our new system and the status of the experiment.

Temperature effects on the optical properties of highly uniform, porous, amorphous ta2o5 coatings on silica

Anghinolfi L, Canepa M, Chincarini A, Chtanov A, Gemme G, Gross M, Neri M, Prato M

We present Spectroscopic Ellipsometry (SE) results, in the 0 : 75 ÷ 5eV spectral range, obtained on Ta2O5 thin films deposited on silica substrates by ion beam sputtering. Two sets of samples with nominal thickness of 40 and 500 nm have been considered. A subset of samples was treated with post- growth annealing in air for several hours at temperatures 300 ◦C < T < 600 ◦C. The SE data have been complemented with Photothermal Common-Path Interferometry at 1064 nm providing information about absorption losses (in the 1 ÷ 4 ppm range). SE data have been analyzed using three different substrate/film/surface models of the fundamental absorption edge, taking into account a graded nano- porosity inside the coating and testing both the shape and the composition of the pores. The best result was obtained by using the Cody-Lorentz model with quasi-uniform density (6 ÷ 7%) of empty spherical pores slowly degrading from the substrate/film interface towards the film/ambient interface. The analysis of SE of films annealed at higher T shows (i) a slight blue-shift of the energy gap (ii) an increase of the pore volume fraction (iii) an increase (1-2%) of the coating thickness (iv) a small (less than 1%) reduction of the index of refraction in the transparency region and (v) a limited increase of absorption losses. These findings are interpreted in terms of a release of the compressive strain induced by the densification intrinsically inherent to the deposition process.

157 Finite element simulations of electromagnetic effects in the advanced virgo payload assembly

Conte A, Chincarini A, Farinon S, Gemme G, Majorana E, Neri M, Puppo P

This work addresses some concerns over a potential noise source that may be relevant for the Ad- vanced VIRGO sensitivity. The electromagnetic interaction among the different parts of the payload (the mechanical structure holding and positioning the mirrors) has undesirable side-effects identified in the dissipation mechanisms due to eddy currents, signal cross-talk among driving coils and magnets misalignment. In order to understand the problem, quantify it and plan for improvement, we have under- taken a series of finite element electromagnetic computations involving significant parts of the payload: the coil disk / marionette and the mirror / cage assemblies. After validating the algorithms on analyt- ical test cases, we have addressed 4 items: (a) the direct coupling of the magnets to an external field, (b) the power dissipation due to the eddy currents caused by the moving magnets in the mirror/cage subsystem, (c) the signal cross-talk among driving coils and their power dissipation and (d) the effect of magnet misalignment. While these are ongoing studies, in this report we present some preliminary results, focusing on their relevance in estimating the noise budget of Advanced Virgo.

In situ correction of mirror surface defects for second and third generation gravitational wave detectors

Vajente G, Day R, Kasprzack M, Marque J

The sensitivity of interferometric gravitational wave detectors depends crucially on the mirror quality. Imperfect mirror surfaces can result in increased round trip losses and coupling of the fundamental mode to higher order modes which are close to resonance. The mirror quality requirements for second generation interferometric detectors are very challenging, and for the use of LG33 modes the polishing accuracy must be improved by an order of magnitude. We present a technique to correct in situ the mirror surface figures by projecting a heat pattern onto the high reflectivity surface of the arm cavity mirrors. This system targets and corrects specific surface figures which are responsible for the coupling to higher order modes. We demonstrate in simulation the performance of the proposed technique and we discuss the application to second and third generation detectors, including discussion of possible sensing schemes to determine the best correction without a priori knowledge of the mirror surface map.

Quadrature fluctuations in a squeezing enhanced full scale gravitational wave interferometer

Dwyer S, Barsotti L, Sigg D, Mavalvala N

Squeezed state injection is one of the most promising techniques to improve the sensitivity of ground based gravitational wave detectors such as Advanced LIGO. Squeezed states have lower noise in one quadrature than a vacuum state, and increased noise in the orthogonal quadrature as required by the uncertainty principle. By replacing the vacuum fluctuations entering the interferometer at the dark port with squeezed states, we can reduce the interferometer quantum noise. Noise from the orthogonal, higher noise quadrature (known as the anti-squeezed quadrature) can add noise to the measurement when there are relative fluctuations between the measured quadrature and the squeezed quadrature (sometimes called squeezing angle jitter or phase noise). These quadrature fluctuations, along with optical losses, limit the utility of squeezed states in gravitational wave detectors. We have modeled several sources of quadrature

158 fluctuations, including cavity length fluctuations, crystal temperature fluctuations and relative alignment fluctuations; characterized the quadrature fluctuations in an Enhanced LIGO interferometer and found them in agreement with our model; and used these results to make projections for achieving more than -6dB of squeezing in Advanced LIGO.

Development of an accelerometer suitable for cryogenic applications leading to 3rd generation gw detectors

Naticchioni L, Frasconi F, Majorana E, Paoletti F

A vertical accelerometer prototype has been developed by re-designing the classical scheme of the sen- sor adopted for the VIRGO interferometer. It is an inertial sensor based upon a floating mass, whose displacement is measured by a positioning sensor (LVDT) that provides error signal suitable for in-loop operation. The vertical acceleration is derived by measuring the feedback voltage current. Thermal contractions are the main concern when cooling down such kind of a device. Compared to other com- mercial high sensitivity accelerometers there is no active electronic component on bord to be hosted at low temperature and just small changes of the readout passive circuit was done. The accelerometer was calibrated at room temperature comparing it with a commercial one, then it was tested and calibrated at cryogenic temperatures. This result was achieved by installing the sensor inside the Vibration Free Cryostat, an active actuator cryostat developed at INFN-Roma1. The accelerometer showed a good response in the low frequency region (0-20Hz) with a sensitivity of the order of 3×10−8V/m/s2. In 2013 the device was successfully installed on the radiation shield of the 2nd KAGRA cryostat, cooled down to 8K measuring its vertical vibration during the cooling tests.

Report on a strong optical spring effect using a high power laser

Fang Q

Optical spring effect is caused by linear coupling of the radiation force on a test mass to a mechanical motion. This effect occurs in optomechanical systems such as Fabry-Perot cavities. It has two aspects in gravitational wave detectors. Without control, it may introduce optomechanical instabilities that could jeopardize detector operation. On the other hand, the optical spring may modify the test mass dynamics therefore makes quantum noise the limiting factor of high detection sensitivity. We will report the study of both aspects of a strong optical spring within a 74-meter Fabry-Perot cavity. The cavity has a finesse of 14500 and two suspended test masses of 0.28 kg each. A 50 W laser will be used as the light source.

Stray light control in kagra

Akutsu T

We report an optical design for stray-light control in KAGRA, the large-scale cryogenic gravitational- wave telescope in Japan, and results of the analysis. KAGRA is an interferometric detector now under construction in the Kamioka mine. As with the other advanced interferometers, KAGRA’s sensitivity will be affected by noises arising from various stray lights, unless which can be reduced by light-absorbing baffles. There are five main types of such baffles. Four types of them are involved in arm cavities of the interferometer, which are the most sensitive to gravitational waves. Each arm measures 3 km long in KAGRA, and an array of less than 125 baffles will be installed. In order to catch wide angle scattering photons from the cavity mirrors, cooled-down wide-angle baffles will be installed very close to them. Narrow-angle baffles for suppressing narrow angle scatterings from the cavity mirrors will be also

159 installed. A cryo-duct shield which helps cooling down an cavity mirror also serves as a baffle array. In addition, a selection process of black materials for the baffle surfaces are reviewed.

Obtaining the deformation noise spectral density for schenberg detector using fem

Bortoli F , Magalhaes N

Schenberg is a spherical resonant mass gravitational wave detector. Its center operation frequency is 3200 Hz. Transducers located on the surface of a resonant sphere according to an semididecahedral distribution, are used to monitor sphere surface displacement amplitudes. The development of mechanical impedance matchers that work as mechanical coupling for the transducers to the sphere in the M´ario Schenberg detector, consists as a challenge for its conception as for its manufacturing, due, to a large extent, for its reduced sizes. For a long time we are developing and optimizing a design for such impedance matchers. The objective of this study is to obtain the deformation noise spectral density and the mechanical amplification for detector Mario Schenberg using such impedance matchers, through finite element modeling (FEM) applying a white noise in one point of the sphere surface and measuring the spectral displacement on the impedance matchers.

Shadow-sensing of violin-modes on an advanced ligo suspension

Lockerbie N

This talk describes the electronics and optical design—and performance in practice—of a low-noise optical shadow-sensor for the detection of Violin- and Pendulum-mode motion of advanced LIGO suspension fibres. Averaged across the set of four sensors, a Violin-mode displacement sensitivity of (69 +/- 13) pm (rms)/ sqrt-Hz, was achieved at 500 Hz, over a measuring span of +/-0.1 mm about the mean position of the suspension fibre under test. This set of sensors was then taken to the LIGO Lab, Gravitational Wave Observatory test facility, at MIT, where it was retrofitted to an advanced LIGO suspension. Violin-Mode and Pendulum-mode signals were recorded there on the four suspension fibres of a fully-suspended 40 kg aluminium-alloy (dummy) test-mass, simulating an advanced LIGO test-mass/mirror. The results of these measurements are discussed.

A low-noise amplifier for shadow-sensing of violin-modes in an advanced ligo suspension

Lockerbie N , Tokmakov K

This poster features the design of an extremely low-noise differential transimpedance amplifier, which senses the photocurrents from two separate photodiode detectors in a Violin-mode shadow-sensor. This novel design of amplifier incorporates features which prevent ’noise-gain peaking’ arising from large area photodiode (and cable) capacitances, and which usefully separate the DC and AC photocurrents from the photodiodes. In consequence, the differential amplifier is able to generate straightforwardly two DC outputs, one per photodiode, as well as a single high-gain output derived from the difference in the photodiodes’ two AC photocurrents. These outputs may be used for the direct calibration of the sensor’s AC displacement sensitivity in terms of volts (rms)/micrometre (rms) displacement of the monitored silica suspension fibre. The results of these measurements are presented.

160 Optomechanical charaterization of silicon nitride membranes

Leonardi M , Zendri J, Prodi G

The sensitivity of the next generation of Earth based gravitational wave detector will be limited in the middle range of frequency by the brownian noise of the coating. In particular, the critical material is the tantalum oxide (Ta2O5). We investigated an alternative material, silicon nitride (SiN), in particular SiN membranes. By investigating the loss angle of the modes of the membranes as a function of the internal stress, we were able to measure the loss angle of the SiN material and to verify quantitatively the dependence of the loss angle from the internal stress of the membrane. The resulting loss angle of SiN is 9.0e-5 with a 5% uncertainty. We extended the investigation to the optical losses of the SiN membranes using a Fabry-Perot cavity with the membrane in the middle. Preliminary results will be presented.

Investigating the atomic structure and properties of mirror coatings for use in future gravitational wave detectors

Bassiri R, Abernathy M, Byer R, Borisenko K, Evans K, Fejer M, Hart M, Kim N, Lin A, MacLaren I, Markosyan A, Martin I, Route R, Rowan S

High performance ion-beam sputtered dielectric coatings are currently being used in the Laser Interfer- ometer Gravitational-wave Observatory (LIGO), and similar ground based interferometric gravitational wave detectors around the world. Mechanical loss in the coatings, which is directly related to Brownian thermal noise, can form an important limit to the sensitivity of these detectors. It has previously been shown that heat-treatment and doping of these coatings can cause noticeable changes to both the optical and mechanical losses. These changes in macroscopic properties are thought to be a result of atomic level structural changes. However, the atomic structure of these materials is not well understood. This is currently an area of intense investigation, as we aim to better understand and ultimately enhance the performance of these coatings. Here we present studies of the atomic structure of amorphous ion-beam sputtered tantala (Ta2O5) coatings. The atomic structure is studied using a combination of Reduced Density Functions (RDFs) from electron diffraction, X-ray Absorption Spectroscopy (XAS), and also Density Functional Theory (DFT) atomic modelling. We show that heat-treatment and doping with titania (TiO2) can induce changes in the atomic structure, which can therefore help to explain the changes observed in the mechanical loss at both room and cryogenic temperatures.

The parametric instability in the kagra

Shibata K , Aso Y, Yamamoto K, Ando M

A parametric instability is the issue where higher order mode, which is not expected to be stored, is stored in arm cavity by the interaction between optical and mechanical modes. When parametric instabilities occur in gravitational wave detectors, higher order modes stored in arm cavities make trouble in locking the interferometers. The instability condition was first obtained in a case of a single Fabry-Perot cavity, and has been extended and applied to gravitational wave detectors. But that condition is not applicable in cases with marginally stable recycling cavities like the KAGRA because of their Gouy phase shifts in them. So we provide a new parametric instability condition which works in any optical configurations in this talk. As an example, we also present a calculated result which estimate the parametric instability in the KAGRA’s update configuration by using the new instability condition, and show that we can decrease risks of parametric instabilities in gravitational wave detectors by changing a few parameters.

161 Optical setup and auto alignment for the frequency reference cavity at the aei 10 m prototype interferometer

Hanke M

The 10 m Prototype facility, currently being set up at the AEI Hannover, will provide a testbed for very sensitive interferometric experiments. One ambitious goal of this project is to reach and subsequently even surpass the ”standard quantum limit” in a detection band around 200 Hz with a 10 m arm length Michelson interferometer. In order to pursue such an avenue, the laser source must be extremely well stabilised. The laser source is a AEI-LZH 35 W Nd:YAG laser also used to drive the km-scale gravitational wave observatories, LIGO and GEO 600. A 23 m long fully suspended triangular ring cavity of finesse ca. 3000 will be used as a frequency reference for the stabilisation of the laser. The aim of this project, the frequency reference cavity, is to reach a level of laser frequency fluctuations of better than 10-5 Hz/sqrt(Hz) in the detection band, centered around 200 Hz. Therefore we need to reduce the frequency noise of the free running laser by a factor of a million. The most important goal is to make a sufficiently stabilised laser beam available for the AEI 10m Prototype Interferometer, with a duty cycle that is not limiting the operation of the core instrument by any means. I will present the optical setup of the frequency reference cavity and the auto alignment for the control of the cavity.

162 C4 - Concepts and Research for Future Detectors

Oral session

Future GW detectors: Concepts and developments

Lueck H

Advanced detectors will go into operation in the next years, promising the detection of a GW signal in the first years of scientific data taking. To open the era of the precision GW astronomy, based on terrestrial detectors, it is necessary to substantially improve the sensitivity of advanced detectors and to develop a new generation of observatories. An overview of the concepts and of the technologies needed for this further improvement is presented.

Optimal network configurations for future gravitational-wave detectors

Raffai P, Gondan L, Heng I, Kelecsenyi N, Logue J, Marka Z, Marka S

We present the results and conclusions of a numerical analysis that aims to find the optimal site locations for possible future networks of 1-3 triangular gravitational-wave detectors. The analysis is based on multidetector figures of merit characterizing the networks’ capability of reconstructing signal polarization, and their accuracy in source localization and source parameter reconstruction. Based on our results, we identify geographical regions where a first, second and third triangular detector could be placed. We also provide a map of potential site locations chosen with respect to basic geographic limitations and expected local noise levels. We use the same approach to suggest an optimal location and orientation for the emerging LIGO-India detector within the five-detector network with Advanced LIGO Hanford and Livingston, Advanced Virgo, and KAGRA.

Newtonian noise subtraction with seismic arrays

Beker M , van den Brand J, Rabeling D

Newtonian noise will limit the low frequency sensitivity of advanced detectors during high seismic activity and will be a dominate limitation to Einstein Telescope’s performance below 7 Hz. Subtraction techniques that involve the monitoring of the seismic motion around the interferometer’s test masses to predict and subtract the resulting Newtonian noise have been proposed. Here, simulation results coupled with

163 measured seismic properties of the Virgo site will be presented. Using optimal filtering in combination with an array of seismic sensors it is shown that significant reduction of Newtonian noise is expected when several hundred sensors are employed. The required self noise of the sensors will be addressed as well as an optimal array configuration.

Characterization of underground seismic noise using 3d seismometer array at the homestake mine

Mandic V

Underground environment is of interest to future gravitational wave detectors due to the reduced seismic noise, and due to correspondingly smaller fluctuations in the local gravitational field, known as the Newtonian noise. Over the past four years, we have built and operated a small array of seismic stations at the Homestake mine, South Dakota. Homestake’s depth and vast horizontal span allow us to probe the seismic wave field over a 1.5 km size cube. We present the most recent results of the analysis of Homestake seismic data, including the applications of Wiener filters to assess the possibility of active suppression of Newtonian noise in a future underground gravitational wave detector. We also present different techniques for estimating the composition of the seismic field based on a limited number of seismic measurements made by a 3D seismometer array. Some of the techniques originate from geophysics and are extended to the 3D configuration, while others are based on the cross-correlation approach already applied in searches for stochastic gravitational-wave background.

Detuned sagnac speedmeter for the 3rd generation gravity wave detectors.

Danilishin S, Voronchev N, Tarabrin S

Sensitivity of the second generation gravity wave (GW) detectors will be limited by quantum fluctuations of light in a wide frequency band and will eventually reach the limit imposed by the counterbalance between shot and radiation pressure noise sources that goes by a well known name of standard quantum limit (SQL). Apparently, third generation detectors are bound to use techniques capable of surpassing the SQL in broad band and known as quantum non-demolition (QND) methods. Speed measurement as opposed to traditional differential arm length sensing is one of such QND tech- niques that allows to reduce radiation pressure noise dramatically. We consider here a realisation of speedmeter based on a zero-area Sagnac interferometer scheme with dual recycling and frequency depen- dent squeezing injection. The specific features of Sagnac interferometer transfer function and dynamics make the requirements on filter cavity loss and bandwidth order of magnitude lower than that of a tradi- tional Michelson interferometer, at the same level of circulating optical power. This implies substantial reduction of infrastructure and core optics price, as well as easier tunability and alignment of the shorter filter cavities.

A realistic polarizing sagnac topology with dc readout for future gravitational wave detectors

Wang M

Current gravitational wave detectors (Advanced LIGO, Advanced Virgo, KAGRA1, and GEO-HF) under construction are implementing techniques based on the Michelson topology, as well as future detectors, such as Einstein Telescope (ET) was planned. We investigate the feasibility of applying a polarizing Sagnac topology to future gravitational wave detectors. We specifically consider the practical issues of

164 a realistic Sagnac based on the ET low frequency parameters, using linear arm cavities and polarizing optics. We show that a realistic Sagnac interferometer with squeezed vacuum input could provide a similar level of radiation pressure suppression but does not require the signal recycling mirror and auxiliary filter cavities. In particular we investigate the effects of non-perfect polarizing optics and propose a new method for the generation of a local oscillator field similar to the DC readout scheme of current detectors.

Observation of three-mode instability in a 10cm optical cavity with a central membrane

Chen X , Zhao C, Ju L, Danilishin S, Blair D, Wang H, Vyatchanin S

Three-mode opto-mechanical parametric interaction in a high finesse optical cavity occurs when the two optical modes couple to an appropriate mechanical mode of the mirrors which have low losses. The phenomenon is highly likely to occur and lead to instability in the advanced gravitational wave detectors because they use high finesse cavities, high laser power and low loss mirrors. We use a tabletop cavity with a silicon nitride membrane acting as a resonator in the middle to study the parametric instability, for the purpose of understanding the phenomena and developing control schemes for large scaled gravitational wave detectors. The TEM00 and TEM02 mode are coupled to the mechanical 26 mode (1718 kHz) and lead to exponential growth of oscillation amplitude. We present observations of spontaneous parametric interaction and parametric instability with different level laser power and different ring-up time. A theoretic model for this phenomenon that is consistent with our results is also presented. The results also shows that the parametric instability may not lead to cavity unlock.

On the feasibility of a vacuum birefringence measurement at a gravitational-wave detector

Grote H

Quantum electrodynamics (QED) predicts that light slows down in the presence of a magnetic field due to virtual electron-positron pair production. Since this effect depends on the polarization direction of the magnetic field with respect to the light field, a birefringence of the vacuum results. A number of experiments have tried to measure this birefringence to date, with the best limit still being a factor 5000 away from the expected effect. It has been proposed to use laser-interferometric gravitational-wave detectors to measure the birefringence of the vacuum, but to date there has been no actual experimental design of such an attempt. I will present some thoughts about possible magnet designs and highlight some implications of such a QED measurement at a gravitational-wave detector.

Laguerre-gauss laser mode research for gravitational wave detectors

Fulda P

As the gravitational wave community strives for ever higher sensitivity from ground based detectors, we are always looking for novel techniques to reduce fundamental noise sources. One such noise source is thermal noise of the test masses themselves, which is expected to limit the sensitivity of Advanced LIGO in the crucial 100Hz frequency region. A possible way of reducing the effects of this noise is to use laser beam shapes with wider intensity profiles, such as higher-order Laguerre-Gauss modes, to better average out the noise over the test mass surfaces. I will present the research program carried out at the University of Birmingham into the feasibility of using higher-order Laguerre-Gauss modes to reduce the thermal noise in gravitational wave detectors.

165 This program has followed a typical new technology evaluation pipeline: from initial simulations, through table-top demonstrations, to experiments at a suspended prototype interferometer in Glasgow.

Measurements of optical absorption in high resistivity silicon for 3rd generation gravitational wave detectors

Bell A, Martin I, Rowan S

The baseline design for the Einstein Telescope, a 3rd generation long base-line interferometric gravita- tional wave detector, calls for the use of cryogenic silicon test masses and an operational wavelength of 1550 nm. Some of the test masses will form the input coupler mirror substrates for the resonant arm cavities of the interferometer. Absorption of the light passing through these substrates will cause loss and may lead to thermal lensing. There is therefore a great interest in determining the optical properties, especially absorption, of silicon at this wavelength. We have undertaken studies of optical absorption in silicon for samples with a range of resitivities from a number of sources/vendors. A common path photothermal interferometer is used to determine refractive index changes caused by a high power pump laser in a sample, using a low power probe read-out laser. Initial measurements indicate absorption val- ues of less than 100 ppm/cm at room temperature at 1530nm. Detailed measurements will be presented as with comparison to measurements of sample resistivity.

Research at lma toward third generation gravitational wave interferometer

Degallaix J

An intensive research effort is on going at LMA in order to characterize coating and subtrates for third generation interferometers. In this talk we will report on the low-frequency measurements of the mechanical loss of a high-quality multilayer dielectric coating of fused silica and titanium-doped tantala, in the 10-300 K temperature range. In parallel to the coating research, we have also measured the intrinsic absorption of bulk silicon below 10 ppm/cm at room temperature.

Amorphous and crystalline coating materials for future gravitational wave detectors

Martin I , Craig K, Rowan S, Cumming A, Murray P, Lin A, Fejer M, Route R, Hough J, Bassiri R, Hart M, MacLaren I, Nawrodt R, Schwarz C, Heinert D

Thermal noise associated with the mechanical dissipation of the mirror coatings is expected to limit the sensitivity of the next generations of gravitational wave detectors at their most sensitive frequencies, with the micro-structure of the coating having been identified as a key factor in determining the loss. An overview of our studies of the physical mechanisms responsible for coating loss will be presented, in particular focusing on initial measurements of tantala coatings using Raman spectroscopy and ongoing studies of the effects of heat-treatment and doping on the loss at cryogenic temperatures. In addition, measurements of possible alternative amorphous coating materials, such as doped hafnia and silicon, will be discussed. We are also studying the mechanical loss of single-crystalline coatings of GaP/AlGaP, a possible alternative to traditional amorphous coatings which can be directly grown on silicon substrates. Preliminary measurements of multilayer stacks of these coatings at cryogenic temperatures are very encouraging, suggesting the loss is at least a factor of ten lower than that of tantala. The results of ongoing measurements of the detailed temperature dependence of the loss of crystalline GaP coatings will be presented, and the likely thermal noise performance of promising candidate coatings for future detectors discussed.

166 Optical tuning and displacement noise of a macroscopic mechanical resonator

Slagmolen B, Nguyen T, Ward R, Shaddock D, McClelland D

We present results of the thermal noise displacement of an aluminium mechanical flexure system, which shows evident of a combination of structural and thermo-elastic damping. The thermo-elastic damping shows a relaxation frequency at which the flexure response exhibit a velocity damped behavior. Away from this frequency the response indicates structural damping. In addition to these results, we present servo controlled optical spring effects. By modifying the locking point, we introduce an optical spring effect and are able to shift the resonant frequency of the mechanical flexure. In addition, by controlling the phase of the feedback signal at the resonant frequency, we command the rigidity of the optical spring and accordingly introducing optical damping.

Anomalous dynamic back-action in interferometers: beyond the scaling law

Tarabrin S, Kaufer H, Khalili F, Schnabel R, Hammerer K

We analyze dynamic optomechanical back-action in the signal-recycled Michelson-Sagnac interferometer with a translucent membrane positioned in its arm, operated off dark port, and reveal its ’anomalous’ features as compared to the ones of ’canonical’ back-action, obtained within the scope of scaling law. Given the finite reflectivity of the membrane, optical damping as a function of detuning acquires (i) non- zero value on cavity resonance and (ii) several stability/instability regions on either side of the resonance. We report on the experimental observation of these instabilities in a Michelson-Sagnac interferometer with a micromechanical membrane. In the case of absolutely reflecting membrane, corresponding to a pure Michelson interferometer, off-dark-port regime results in several intersecting regions of positive/negative values of optical spring and damping. For a certain region of parameters, stable sets of both effects in a free-mass interferometer with a single laser drive are possible. Our results can find implementations in both cavity optomechanics, revealing new regimes of cooling of micromechanical oscillators, and in the gravitational-wave detectors, revealing the possibility of stable single-carrier optical spring which can be utilized for the reduction of quantum noise in future-generation detectors.

Single sideband angular deflection gravitational wave detector

Blair D

It is shown that a long baseline interferometer can be configured to detect gravitational waves through the angular component of the gravitational wave strain. The angular deflection interferometer operates through a three-mode interaction which upconverts the gravitational wave energy into a single upper sideband. The detector requires a signal recycling Fabry-Perot interferometer in which a TEM01 mode is tuned to Ωo + Ωg where Omega0 is the pump laser frequency and Omegag is the gravitational wave signal frequency. The angular signal appears in the differential output of the beamsplitter while the dominant technical noise source, beam jitter noise, is common mode. An angular optical spring allows the detector to exceed the free mass standard quantum limit. If located in the same vacuum system as a conventional interferometer, the detector is intrinsically sensitive to the orthogonal polarisation, thereby enabling full waveform sampling within the common sensitivity bandwidth of such a dual instrument.

167 Juggling interferometer for the detection of gravitational waves

Friedrich D, Kawamura H, Hirobayashi S, Kawamura S

We investigate a novel type of earthbound gravitational wave detector targeting a frequency band around 1Hz. The test mass mirrors of the currently build advanced laser interferometric detectors are realized as multi-stage suspension systems that are designed to provide seismic isolation starting from around 1Hz. Consequently, theses detectors are limited by seismic noise and suspension thermal noise in their lower frequency band. By using free falling test masses one can in principle decouple test masses from the seismically noisy environment in a straightforward manner. Our approach utilizes repeatedly free falling test masses, in order to increase the actual measurement time and thereby the frequency resolution to search for continuous low frequency signals. However, in this type of measurement - we call this a juggling interferometer - the initial conditions of the test masses, such as their microscopic position and initial velocity, will differ in each measurement cycle, leading to discontinuous data. Here, we will discuss the numerical results of a dedicated matched filter algorithm that is used to analyze the data. The applied method allows to preserve a given sensitivity in the presence of discontinuities down to frequencies that are determined by the inverse of the free fall time.

168 Poster session

Noise modelling for atom interferometry

Palmer R, Rocco E, Bongs K, Freise A

Atom interferometry can measure gravity with potentially very high precision; it has been used to mea- sure the gravitational constant G, and has been proposed as a space-based gravitational wave detector. However, reaching this precision requires careful minimisation of many noise sources, including shot noise, laser frequency noise, wavefront distortions, and rotational vibration. We develop a computer model of atom interferometry and its errors, that can be used to optimise the interferometer’s design for minimum noise. In particular, we use tools from optical gravitational wave detection to simulate in detail the laser wavefront distortions from realistically imperfect optics. We use this model to investigate using a detection aperture or image-forming detector to suppress or subtract off noises caused by imperfect control of the atom clouds’ position and size, including wavefront distortion and Coriolis (rotation) effects.

Study of six mechanical two-mode impedance matchers on a spherical gravitational wave detector using fem

Frajuca C , Magalhaes N

A spherical gravitational wave (GW) detector has a heavy ball-shaped mass which vibrates when a GW passes through it. Such motion is monitored by transducers and its respective electronic signal is digitally analyzed. One of such detectors – Schenberg - will have resonant frequencies around 3.2 kHz making the transducer development for this higher frequency detector somewhat more complex. In this work we present a series of finite study elements of a sphere coupled to two-mode mechanical oscillators that will work as mechanical impedance matchers between the sphere and the microwave transducer. We describe the search for a shape of the impedance matcher that might improve the performance of the detector. We found that the normal modes of the coupled system are not exactly degenerative, although theoretical calculation predicts that they should be. This work also reports improvements made in the modelling of mechanical impedance matchers using finite elements method when shell elements type were used instead of tetrahedron elements type, showing that method works as a very good approximation.

169 Issues for suggested single photon recoil atom interferometry gravitational wave measurements in space

Bender P

P. W. Graham et al. have suggested GW measurements in space using atom interferometers based on single photon transitions [PRL 110, 171102 (2013)]. The main example given is based on the Sr-87 698 nm clock transition, L = 1000 km spacecraft separation, N=300 LMT beamsplitters, and 2T = 100 s measurement time. However, there appear to be a number of issues for discussion concerning the proposed approach. 1) If confocal laser beams are used, a Rabi frequency of at least 200 Hz would require 50 W or more of laser power and roughly 1 m diam. telescopes. 2) For this case, an atom cloud temperature of about 1 pK would be needed. 3) The number of atoms required per cloud to reach 10−20/(Hz0.5) sensitivity at 0.01 Hz is about 109, even if about 25 atom interferometers can be run concurrently. 4) Achieving the survival of 1200 velocity state transitions for each part of the atom wavefunction is challenging; the best achieved so far appears to be less than 200. 5) Common but large phase shifts between the 2 parts of the wave function will be present in each interferometer due to laser pulse timing jitter. 6) If isotopes with nuclear magnetic moments are used, measurements have to be made nearly simultaneously with atoms in different nuclear spin states. 7) 200 m sun shields for the atoms appear to be needed. 8) Laser beam intensity differences between the two interferometers coupled with small variations in the laser frequencies and micron/sec mean velocity variations for the atom clouds can produce significant differences in the amplitudes for the two parts of the wave function. 9) The required apparatus for the suggested type of mission is extremely complex.

Searching for 3-mode parametric instabilities on gingin high optical power facility

Zhao C , Fang Q, Blair C, Ju L, Dumas J, Blair D

A high finesse high optical power cavity has been built at Gingin, Western Australia for studying 3-mode parametric instabilities and their control. The cavity consists of two fused silica test masses of 100mm in diameter and 50mm thick, radii of curvature of 37.4m and 37.5m respectively. The cavity length is about 73.6m. The cavity is initially locked to a 500mW Nd:YAG laser. The measured cavity finesse is 14600+/-300. The characterisation of the test mass acoustic modes is in progress. A 50W fibre laser amplifier has been installed to increase the input power. We expect to build up 100kW circulating power inside the cavity and to observe the high gain parametric instabilities. The most recent results will be presented.

Dynamic tuning for a signal recycled interferometer.

Simakov D

In this work we study a particular method of detection of the chirp signal, the so-called dynamic tuning. The exact simulation of the detector response for the arbitrary signal recycling tuning variation and input signal is performed. Using the response, we calculate the shot noise and prove that it stays white for non-stationary regimes of interferometer operation. This allows us to compute the signal-to-noise ratio of the detection with dynamic tuning. The problem of signal deconvolution is also solved.

170 Results of the medium size ring-lasers g-pisa and gp2

Di Virgilio A, Calamai M, Belfi J, Beverini N, Cuccato D, Carelli G, Maccioni E, Ortolan A, Santagata R

G-Pisa is a ring-laser which is kept in continuous operation by active control, with typical sensitivity of the order of few nrad/s in 1 s measurements. It can be used as a tilt-meter. It has been installed inside the Virgo central area in the 2011 and more recently inside the GranSasso underground INFN laboratory. The measurements taken by G-Pisa are presented and discussed, with special attention to the application of Kalman filter to reduce the systematic effect coming from the back-scattering, which limits the response of the ringlaser below mHz. GP-2 the new prototype based on the experience of G-Pisa will be discussed.

Sideways motion of reflective waveguides for use in advanced gravitational wave detectors

Leavey S

The current ground-based gravitational wave detectors are limited in their performance by Brownian thermal noise associated with the coatings used on the multi-layer dielectric mirrors on the front surfaces of their test masses. One way to reduce such noise is to get rid of the multi-layer coatings altogether, and it has been shown that coating-free waveguide mirrors can reduce the total noise budget, particularly at cryogenic temperatures. The use of highly reflective waveguides in future interferometers is an active area of research, and the results of an experiment at the University of Glasgow looking into the coupling of the waveguides’ transverse motion into the gravitational wave signal channel will be presented.

Comparison of michelson- and sagnac-interferometers regarding their susceptibility to mirror imperfections

Huttner S

In resent years the Sagnac-interferometer became more interesting for the GW-community. The Sagnac- and Michelson-interferometers with arm cavities differ in their fundamental operation. The Sagnac- interferometer employs ring-cavities in the arms where the light runs clock- and anti-clock wise, and in the Michelson-interferometer the light is enhanced by FP-cavities. We look how these differences influence the susceptibility to mirror imperfections, by comparing the mode-matched interferometers with the case of imperfect mode-matching.

Modelling mirror surface distortion effects in low-loss, near-unstable fabry-perot cavities

Brown D

Gravitational wave detectors utilise optical cavities in several ways. When squeezed light is injected to reduce the quantum noise, optical losses can significantly degrade its effects, in particular losses in the arm and filter cavities . At the same time, mirror thermal noise can be reduced by increasing the spot size on the mirrors leading to near-unstable cavity geometries. We use numerical models to investigate such low-loss, near-unstable cavities, notably the effects of nanoscale defects present on the mirror surfaces on the cavity performance.

171 The detection of gravitational waves using electrodynamic system of earth

Grunskaya L, Isakevich V, Rubay D

The work is connected with studying electromagnetic fields in the resonator Earth-Ionosphere. There is studied the interconnection of tide processes of geophysical and astrophysical origin with the Earth elec- tromagnetic fields. The monitoring of electrical and geomagnetic fields of ELF range of the atmosphere boundary surface layer is provided at the spaced apart stations: Vladimir State physical experimental ground; the station of RAS Institute of Sun and Earth physics at Lake Baikal; the station in Paratunka (Kamchatka); the station in Obninsk. There has been developed a programme-analytical system (PAS) to investigate signal structures in spectral and time series, caused by geophysical and astrophysical processes based on the method of eigen vectors. The problem of the anomalous behavior of the elec- trodynamic system response to the gravitational – wave affect is being discussed. On the basis of the rich experimental material have been investigated the frequencies of gravitational–wave radiation of a number of binary systems: J0700+6418, J1012+5307, J1537+1155. The work is carried out with sup- porting of RFFI 2116˘ 11-05-97518, FPP 211614.B37.21.0668.,˘ FPP 21165.2971.2011˘ Report is based on the papers: 1.Grunskaya L.V.,Efimov V.A., Isakevich V.V.,Zakirov A.A. Experimental investigations of the interaction between the ELF Earth electromagnetic fields and astrophysical processes. //American Institute of Physics AIP Conf. Proc.–2010.-V.1206.-p.455-461.

Long term seismic characterization of candidate sites for the et: preliminary analysis and results in sos enattos mine

Acernese F , Romano R, Giordano G, Barone F, De Rosa R, Naticchioni L, Majorana E, Perciballi M, Puppo P, Rapagnani P, Ricci F, Punturo M, Malvezzi V, Fafone V, Rocci A, Coccia E, Loddo L, Calia P

The knowledge of seismic behaviour in the microseismic and anthropogenic band (20 mHz - 20 Hz) at different underground levels is essential for the characterization of candidates sites to host third generation of gravitational wave detectors, like the Einstein Telescope (ET). From preliminary analysis Sos Enattos mine, Sardinia (Italy), is one of the candidates sites for hosting ET, that deserves particular attention due to low seismic activity and intrinsic environmental stability well within the ET requirements. Following these preliminary results, we started a campaign of measurements in the Sos Enattos mine aimed to the long term seismic characterization of the site, at different underground levels. For this task we designed and implemented a modular monitoring system composed, at this first stage, by three stations connected among them through optical fibres: the first one is located at ground level (338m above sea level) and is equipped with an environmental monitoring system for correlating the weather conditions and the surface seismic noise with the underground seismic noise; the second one, at about -84m underground level, and the third one, at about -111m underground level, are each equipped with an environmental monitoring system and with several high sensitive seismometers. The results of the first months of data taking relative to seismic noise measurement at different underground levels, correlated to the meteorological data, are presented and discussed.

A new control approach for the implementation of low frequency large band seismic suspensions and inertial platforms

Barone F , Acernese F, Canonico R, De Rosa R, Giordano G, Romano R

Low frequency seismic suspensions (attenuators) and inertial platforms require a careful design not only of the mechanical attenuation stages but also of the control system, especially if a residual horizontal motion

172 better than 10-15 m/sqrt(Hz) in the band 0.01 - 100 Hz is a requirement. One of the most important element of the control system is the tipology of the sensors, whose accuracy, stability, sensitivity and band may constitute a real limitation for the improvement of their performances, especially if very large seismic attenuations are required in the low frequency band. In particular, the present most effective control systems, based on accelerometric sensors (force feed-back configuration), are mainly limited by the sensor electronics. To try improve the performances of low frequency suspensions (attenuators) and inertial platforms, we introduced a new control philosophy: the control system directly acquires the instantaneous relative positions of the mechanical components trough monolithic folded pendulum sensors without any force feed-back (seismometer configuration). In the paper we discuss this new control architecture and the results of the tests on a state-of-the-art mechanical suspension.

Low frequency/high sensitivity triaxial monolithic sensor

Barone F , Acernese F, Romano R, Giordano G, De Rosa R, Canonico R

This paper describes a completely new mechanical implementation of a monolithic triaxial inertial sensor, configurable both as seismometer (open loop) and as accelerometer. The sensor is compact, light, scalable, tunable (horizontal frequency < 100mHz; vertical frequency < 1Hz), with large band (10−7Hz−10Hz), high quality factor (Q > 1500 in air) instrument and good immunity to environmental noises, guaranteed by an integrated laser optical readout.√ The measured sensitivity curve is in very good agreement with the theoretical ones (10−12m/ Hz in the band (0.1 − 10Hz). Typical applications are in the field of earthquake engineering, geophysics, and in all the applications that requiring large band-low frequency performances coupled with high sensitivities are required, including control applications.

Optical absorption measurements on a crystalline silicon test mass at 1550 nm

Steinlechner J , Khalaidovski A, Kr¨ugerC, Schnabel R

Today’s gravitational wave detectors (GWDs) use a laser wavelength of 1064 nm and test-mass mirrors made from fused silica. Future GWDs such as the Einstein Telescope consider cryogenic cooling of the test-masses to reduce their thermal noise. Due to its high mechanical quality factor at low temperatures and a high heat conductivity, silicon is a promising new test-mass material. An important question is whether the optical absorption of silicon is low enough since some of the test- asses require transmission of intense laser radiation. At 1550 nm silicon is expected to show a rather low optical absorption, however, precise absorption coefficients are not known. This poster presents absorption measurements on a crystalline silicon test-mass at 1550 nm. For these measurements the photo-thermal self-phase modulation technique (PSM) was used. PSM was especially developed for absorption measurements on substrates resembling GWD mirror test-masses. A distinct feature of our technique is that surface effects are included in the absorption measurements.

Quantum-dense readout for gravitational wave detectors

Steinlechner S, Bauchrowitz J, Meinders M, Mueller-Ebhardt H, Danzmann K, Schnabel R

The high-frequency sensitivity of interferometric gravitational-wave detectors is limited by the light’s quantum noise, i.e. shot-noise arising from zero-point fluctuations at the detection dark-port. Non- classical, squeezed-light readout can reduce this noise and has been successfully implemented in GEO600 and was recently also tested in LIGO. In the mid-frequency region, the quantum noise is obscured by both

173 thermal noise and parasitic interferences due to scattered light. Here we present a novel quantum-dense interferometer readout scheme, which we implemented in a table-top experiment. This scheme is able to identify and possibly remove parasitic signals, thus increasing the detection sensitivity in frequency bands that were previously not quantum-noise limited.

Non-ideal coherent noise cancellation for quantum optical systems

Denker T , Sch¨utte D, Wimmer M, Heurs M, Danzmann K

The future generation of laser interferometric gravitational wave detectors will be limited in sensitivity by radiation pressure noise (RPN) in the frequency range from 10 to 100 Hz. Next to shot noise this is the other fundamental noise source caused by the quantum nature of light. The temporally statistically distributed photons of a light field push on a cavity mirror and the back action caused by the restoring force imprints a phase shift on the light field. This effect acts as a phase modulation, masking the effect of a gravitational wave. To reduce the effect of RPN we want to employ coherent control schemes and present a possible experimental realisation of coherent feed-forward. It consists of a meter cavity with an opto- mechanically coupled mirror that exerts back action on the cavity light field due to RPN. To eliminate the back action an auxiliary cavity that acts as a ”virtual negative mass oscillator” is introduced to destructively interfere with the RPN before the resulting light field leaves the meter cavity. The coupling between the two cavities can be realised by a beamsplitter and an optical parametric amplifier (OPA) in the auxiliary cavity which produces the required ”anti-noise”. By choosing the right parameters for the OPA and appropriate efficiencies it is possible to achieve radiation pressure noise cancellation. I will talk about theoretical possibilities and limitations.

An optical spring with an intra-cavity sqeezer

Kato J , Sakihama Y, Westphal T, Goßler S, Somiya K

Sensitivity of the interferometric gravitational wave detectors will be limited by the standard quantum limit (SQL). Detuning the cavity, radiation pressure induces the optical spring. At its resonant frequency, the sensitivity will enhance and overcome the SQL. For the next stage, we would like to obtain the high sensitivity not only at resonant frequency but in broad band. I suggest that the squeezer which depends on frequency be installed in the cavity so that at every frequency, the optical spring will be resonant. For proving this technique, we make a prototype dual recycling interferometer using 300mg mirrors suspended by cupper wires. We will observe radiation pressure effects.

Development of a low-frequency gravitational-force sensor

Slagmolen B, Adhikari R, Rowan S, McClelland D

We present the design concept of a low-frequency gravitational-forces sensor. The sensor is targeted for sensing the Newtonian noise due to atmospheric and seismic disturbances at frequencies below 10 Hz. The sensitivity of future gravitational wave detectors will be limited by these noise contributions. The low-frequency gravitational-force sensor can provide an independent measure of the Newtonian Noise to validate the estimator in the future Newtonian Noise cancellation systems.

174 The sensor design is based on the torsion bar antennae, developed by Ando (National Astronomical Observatory Japan). The low-frequency gravitational-force sensor consists of two perpendicular beams, independently suspended as torsion pendulums. They share the same suspension point, have their axis of rotation co-linear and center-of-mass co-incident. An incoming gravitational gradient (in the same plane as the two suspended beams), will rotate the beams differentially. The linear distance between the ends of the beams, Lx and Ly, will change and are measured using a Michelson interferometer. Any linear pendulum motion between the beams is be registered as a common mode motion, to which the Michelson is mostly insensitive. We will show a mechanical design and present modeled sensitivity performances.

Active damping of triple-suspended mirror for the 10m prototype via modern control techniques

Schuette D, Denker T, Wimmer M, Heurs M, Danzmann K

Modern control techniques ease the design process of feedback loops needed to control and stabilise complex systems. We show that active damping of the suspensions can be accomplished via an Linear Quadratic Gaussian controller. This controller combines a Linear Quadratic Regulator (LQR) and a linear time-invariant Kalman filter. The LQR characterises the overall system dynamics, including unwanted cross-correlations for the six degrees of freedom in form of a state space model. The LQR solves a cost functional minimising the quadratic sum of the position fluctuations of the suspended mirror for a specific control energy. The Kalman filter optimally estimates non-measurable variables and adds white Gaussian noise to the measured signals. To determine the frequency response of the system we set up an optical lever to read out the motion of the lower stage after introducing a signal at the top stage. This readout also provides the possibility to identify non-ideal suspension setups. As a result the combination of passive damping, suspension design realised by the 10m prototype group, and active damping of the eigenmodes of the triple pendulum should enable the desired performance for interferometric measurements at the Standard Quantum Limit.

A path length modulation technique for frequency shifting scatter induced noise in squeezing measurements

Wade A, Chua S, Stefszky M, Shaddock D, McClelland D

Spurious scattered light reflections couple low frequency environmental noise into the homodyne measure- ment of squeezed light states. We present a technique for frequency shifting contributions of scattered- induced noise in squeezed light measurements. By pre-modulating the path laser pump path length at the start of the squeezing apparatus followed by a matched antisymmetric post-modulation, a vacuum squeezing ellipse is kept in a fixed quadrature whilst modulating the phase of reflections originating between the two points of modulation. A 500 Hz sinusoidal path length dither is implemented, matching the phase and depth of dither of two mirrors. We show a 20 dB reduction in scatter-induced noise in a balanced homodyne measurement of a squeezed vacuum state, recovering squeezing down to the 1 Hz level. Such a technique offers advantages improving scatter immunity without the need for lossy isolat- ing optics that degrade the degree of squeezing. A path length modulation technique actively reduces contributions from scatter within a squeezing apparatus path and is potentially useful for squeezing deployments to laser interferometer gravitation wave detectors where it is desirable to frequency shift spurious back reflections coupling in through a squeezing injection port.

175 Control of the angular motion of the tiny 20mg suspended mirror in the high power cavity for qrpn measurement.

Nakano M , Friedrich D, Agatsuma K, Sakata S, Miyakawa O, Furusawa A, Kawamura S, Kuroda K

The radiation pressure noise (RPN), which arises from the quantum intensity fluctuation, will limit the sensitivity of the advanced gravitational wave detectors like KAGRA. Hence, the development of experimental techniques to reduce the RPN is highly interesting. In our experiment, we challenge to construct a table-top system to observe the RPN and verify the technique to reduce it by taking advantage of the phenomenon called ”ponderomotive squeezing”. When the laser light is reflected off a suspended mirror, the quantum fluctuation of the laser light is squeezed by the non-linearity of the mirror movement caused by the intensity fluctuation of the light. Consequently one can reduce the RPN using a homodyne readout scheme with optimized homodyne angle. This technique will be applied for the final stage of KAGRA, thereby beating the standard quantum limit. We are developing a Fabry-Perot Michelson interferometer using tiny 20mg end mirrors in order to observe the RPN. Currently we are investigating the control of the angular instability of a single cavity. The latter one arises due to the high circulating laser power required for observing the RPN. In our approach, the cavity axis is controlled by the angular alignment of the front mirror respect to the small mirror, thereby we can avoid the small mirrors angular motion to become unstable. The angular behavior of the optical cavity as measured in the experiment qualitatively agrees with the optomechanical control model.

Coating thermal noise interferometer

Westphal T , for the AEI 10m Prototype team

Coating thermal noise (CTN) is becoming a more and more significant noise source as the sensitivity of interferometry is pushed to its limits. It arises from inherent mechanical loss of thin films in dielectric coatings. Deeper understanding and verification of its theory such as frequency dependence of losses requires direct (off-resonant) observation. The AEI 10 m Prototype facility is probably the best suited environment for this kind of experiment in a frequency range of special importance for earth bound gravitational wave detectors. A pre-isolated platform shows three to four orders of magnitude attenuated seismic noise inside an ultra-high vacuum system. Up to 10 W highly stabilized (in frequency as well as amplitude) laser power at 1064 nm will be available for experiments. In this talk the CTN- interferometer, being in the construction phase, will be presented. The range that is solely limited by CTN is designed to reach from 10 Hz to about 50 kHz, limited by seismic noise at low frequencies and shot noise (photon counting noise) at high frequencies. The first of three identical suspensions has been set up. Digitally controlled actuation as well as active damping were sucessfully demonstrated.

Design and development of a suspension platform interferometer for the aei 10m prototype interferometer

Koehlenbeck S, for the AEI 10m Prototype team

The AEI 10m Prototype interferometer is a facility for developing and testing novel techniques for ad- vanced gravitational wave detectors. It is also an environment for performing measurements at and beyond the standard quantum limit (SQL). Therefore, a vacuum system with a volume of 100mlin an L shaped configuration is installed to house experiments, such as the sub-SQL interferometer. Three optical

176 tables are placed inside the vacuum envelope. The optical tables are suspended by pendulum stages to isolate the experiments from seismic motion. These isolation benches are referred to as AEI-SAS (seismic attenuation systems). Below the resonance frequency of the pendulums the optical tables are not decou- pled from the ground motion. Hence, we have designed and built a suspension platform interferometer (SPI) to stabilize the differential table motion in the frequency range from 10mHz to 100mHz down to 100pm/sqrt(Hz) in longitudinal displacement and 10nrad/sqrt(Hz) in angular displacement. The SPI senses the relative motion of the three SAS in five degrees of freedom by heterodyne interferometry and differential wavefront sensing. The interferometric signals are used in a feedback control system to stabilize the SAS relative to each other, so that one rigid platform is formed. The design of the SPI and the first measurements will be presented.

Digital control and data system of the aei 10m prototype interferometer

Born M , for the AEI 10m Prototype team

The AEI 10m Prototype Interferometer uses an aLIGO control and data system (CDS). This poster presents the current status of the system at the AEI and its specific features. The use of a digital interface (PMI) for an AEI LISA Pathfinder Phasemeter is emphasized. Digital timing jitter and the resampling of up to 100 data channels in real time are challenges introduced by the PMI. Possible solutions are analyzed and presented.

The aei-sas: seismic isolation for the 10m prototype interferometer

Bergmann G, for the 10m Prototype team

A 10m arm length prototype interferometer is currently being setup at the AEI in Hannover, Germany. This facility will not only be used for developing novel techniques for future gravitational wave detectors, but furthermore it will provide a platform for high precision experiments such as measuring the stan- dard quantum limit (SQL) of interferometry. To achieve the high requirements on displacement noise for these experiments a very good isolation from seismic motionis required. Here we present the pre- isolation stage for the 10m prototype interferometer based on a set of passively isolated optical tables. Geometricanti-spring lters provide vertical isolation, attenuation in the horizontal direction is provided by inverted pendulum legs. Several sensors and a Suspension Platform Interferometer will be used to measure theresidual table motion. These signals will be used to control the tables at and below their fundamental resonances. Attenuation of more than 60dB below 10Hz was shown in rst experiments with purelymechanically passive isolation. Currently two out of three tables are installed in the interferometer vacuum envelope.

177 C5 - Space Based Detectors

Oral session

The completed optical bench interferometer for lisa pathfinder

Killow C , Fitzsimons E, Perreur-Lloyd M, Robertson D, Ward H

The flight optical bench interferometer (OBI) for LISA Pathfinder has been delivered by the UK to Astrium GmbH for integration into the LISA Technology Package Core Assembly. This talk will discuss the function, design, construction and testing of the OBI. We will also highlight the advances made towards realising the optical sensing for a spaceborne gravitational wave detector that have been made as a result of this work.

Performance testing of the lpf optical metrology system

McNamara P, Gerndt R, Hechenblaikner G, Flatscher R, Hewiston M

As part of the LISA Pathfinder On-Station Thermal Test campaign, the performance of the flight optical metrology system (OMS) was measured. This was the first full system level test of the integrated flight hardware of the OMS. The test was made possible by the use of the Thermal Optical Qualification Model (TOQM) in place of the LTP Core Assembly. The TOQM consists the flight optical bench and associated mounting hardware, coupled with thermal/mass dummies of the inertial sensors, incorporating mirrors in place of the test masses. Several performance runs were made, both at hot and cold operating temperature extremes. In all cases the OMS performance was shown to meet, and significantly exceed, the imposed requirements. In this presentation, we will introduce the LTP optical metrology system, followed by a description of the On-Station Thermal Test. The results achieved will be presented, including the overall simulated performance of the LPF mission assuming this level of OMS performance. Finally the limiting noise sources will be described, with possible mitigation strategies identified.

Geodesic reference masses for lisa pathfinder, elisa, and beyond

Weber W

Free-falling geodesic reference test masses are the core of many experiments in gravitation and in partic- ular for gravitational wave observation. LISA Pathfinder is the flagship mission for reference test mass metrology, aiming to demonstrate macroscopic test masses in free-fall with a residual acceleration noise

178 below femto-g/sqrt(Hz) at mHz frequencies. This talk aims to share our experimental experience in the design and ground testing of the LPF gravitational reference system, with torsion pendulum small force measurements at the femtoNewton level. We will apply our studies to the fundamental limits in the low frequency resolution of the eLISA gravitational wave observatory and then extend our findings to the use of macroscopic reference test masses in future gravitational missions over a range of frequencies and performance requirements.

Science and mission scenarios for a saddle point test of modified gravity with lisa pathfinder

Sumner T, Armano M

Several dark matter/energy models and many modifications of Newton’s and Einstein’s theories (co)exist today to better match observations at controlled extra costs. No conclusive astrophysical measurements favour one approach over the other and a null test based on dynamics at the crossing between the Newtonian regime and the next undiscovered country is still missing. The LISA Pathfinder spacecraft is on schedule to fly by the end of 2015. Besides being a downscaled in-flight test for a ”LISA/NGO” gravitational cosmology observatory, its core sensor, made of two test masses in mutual free-fall with interferometric position tracking, makes it a space-borne gradiometer of unprecedented precision. Possible enhancements of the mission after the originally design measurement phase could explore gravity at its alleged depart from the Newtonian regime: orbit trajectories studies show that LISA Pathfinder is capable of cruising near the saddle point of the Sun-Earth system, a volume of space where Newtonian pulls compensate and the Newtonian acceleration is close to zero. We will explicitly consider MOND as a test theory and show that the spacecraft would sample several scales of the Newtonian-MONDian regime, possibly reducing its parameter space. We shall concentrate on the science case, the mission design, its feasibility study and operations scenario, leaving the in-depth data analysis assessment to our sibling presentation.

Elisa science

Sesana A

In the coming years the detection of gravitational waves (GW) will be a reality, opening a completely new window on the Universe. Ground based detectors like the Advanced LIGO will observe coalescing compact binaries out to hundreds of megaparsecs, revealing the hidden face of the local Universe. At lower frequencies, future space based interferometers will primary target inspiralling and coalescing massive black hole binaries throughout the Universe. eLISA is a concept proposed to ESA for the L1 downselection. The mission has been re-proposed in the context of the L2/L3 downselection. I will briefly describe the design of the mission, the relevant astrophysical GW sources, and the multiple scientific payouts of detection.

Technology developments for future space based gw missions

Jennrich O

Space based gravitational wave missions present numerous technical challenges. The European Space Agency is running a number of activities that are aimed at developing and consolidating the key tech- nologies for gravitational wave detectors. This talk will present the current status and teh future outlook on these activities.

179 Periodic orbit control maneuvers for the elisa mission

Bender P

The eLISA mission that is now being studied as a candidate for the ESA L-2 mission has an arm length of one million km between the spacecraft, compared with five million km for the original LISA mission. In addition, the use of a technique called in-field guiding to allow for variations in the angles between the lines-of-sight to the different spacecraft is being considered, in order to simplify the spacecraft design. The shorter distances between spacecraft make it easier to use periodic orbit corrections to keep the angles of interest from increasing with time due to tidal forces from the Earth. Thus, as discussed at the LISA 9 Symposium, the thrust required in order to keep the angle variations down to plus and minus 0.1 degree over the life of the mission has been investigated. With roughly the level of thrust expected to be available on the spacecraft, it appears that this angle stabilization goal can be achieved with only a few percent loss in the available science observation time during the mission. The required thrusts would be applied roughly every 6 days, when other spacecraft operations such as rotation of the communications antennas and optical system checks would need to be performed. The extra amount of thruster fuel required would be fairly small. The considerably reduced range of angle variations that would need to be corrected for by an in-field guiding system would make avoiding jitter in the laser beam path lengths substantially simpler.

Gravitational wave astrophysics; the next frontier in understanding the universe

Buchman S, Byer R, Lipa J

Astrophysics, our present understanding of the Universe, rests primarily on imaging in the electromag- netic spectrum, spanning radio to gamma ray astronomy. ’Visible’ matter generating photons represents only about 0.4% of the total mass of the Universe, with dark energy 73%, dark matter 23% and in- tergalactic gas 3.6% constituting the rest. Of the four fundamental forces two are long range allowing remote observation; electromagnetism, carried by photons, and gravitation, carried by gravitons. Pho- tons are an important but incomplete source of information, as they are generated by ’secondary’ forces in 0.4% of matter, are readily absorbed and/or scattered, are only weekly influenced by gravitation and do not interact with dark matter and dark energy - believed to make up 96% of all matter. Over the last three decades, an exceptionally good science case has been made for pursuing gravitational wave (GW) astronomy. This has engendered a worldwide effort to detect the extremely weak signals gener- ated by expected sources. With the next round of upgrades the ground based instruments are likely to make the first detections of the sources, and a new era of astronomy will begin, possibly as early as 2017. Inconveniently, due to seismic noise and baseline length issues, the low frequency (¡10Hz) part of the spectrum, where the most interesting events are expected, will not be accessible. The space-based detector LISA was conceived to fill this gap extending the observational capability to about 0.1 mHz. Due to mission cost growth and severe budget constraints, a flight prior to 2030 now seems very unlikely. However, a 30-year program in low frequency GW astronomy should set as its goal the development and implementation of three generations of space antennas, one per decade, with an absolute minimum requirement of two generations. This would allow getting science data early in the next decade, keeping the next observatories open to new technology advances and engaging in a robust parallel technology development program on the ground and on small satellites. For the ’first’ decade observatory we make the case for a scaled down mission, of the LISA 2020 type, that is comparable in cost and duration to medium scale astrophysics missions such as the 1978 ($630M) Einstein (HEAO 2) x-ray Observatory , the 1989 ($680M) COBE Cosmic Background Explorer , and the 1999 ($420M) FUSE Far Ultraviolet Spectroscopic Explorer . We find that a mission of this class is possible if the measurement requirements are somewhat relaxed and a baseline smaller than LISA is used. Such a mission could be launched by 2020 using a conventional program development plan, possibly including international collaboration .

180 It would enable the timely development of this game-changing field of astrophysics, complementing the expected ground results with observations of massive black hole binary systems. It would also serve as a stepping stone to the next missions, greatly reducing their risk profile. LISA-2020 is based on three principles: a) aim for the core science, the merger of supermassive black hole binaries; it has the greatest intellectual return and, fortuitously, requires easier technology b) develop and test critical technologies in parallel, utilize alternative approaches where required and take advantage of the modern capabilities of small and nano-satellites; each team of your marching army solves its own problem and the overall program starts when all technology is in hand, c) engage the international community in the effort, using both conventional and non-conventional partners; this science program is literally a ’new vision for humanity’ and should be approached as such. A ’second’ decade observatory could be either an enhanced LISA-type technology observatory (the more ambitious and costly eLISA , or an upgraded version thereof) or an instrument based on alternative technologies; if available on a timely basis. For the ’third’ decade observatory one would expect new technologies and approaches for very high precision measurements to dominate the design. Technology development for second and third generation low frequency GW antennas would proceed in parallel with the implementation of the previous instruments. We discuss the LISA-2020 design and the enabling technology development, both in the laboratory and through small and nano-satellite flights.

Breadboard model of the lisa phasemeter

Gerberding O, Barke S, Brause N, Bykov I, Danzmann K, Enggaard A, Gianolio A, Hansen T, Heinzel G, Hornstrup A, Jennrich O, Kullmann J, Pedersen S, Rasmussen T, Reiche J, Sodnik Z, Suess M

The detection of gravitational waves in the sub-Hz regime will allow insight into the dynamics of binary systems and galactic objects, like mergers of ultra-massive black holes. For this purpose the space-born gravitational wave detector LISA is planned, which uses precision heterodyne laser interferometry as main measurement technology. A breadboard model for the phase readout system of these interferometers (Phasemeter) is currently under development as an ESA project by a collaboration between the Albert-Einstein Institute, the Technical University of Denmark and Axcon Aps. The breadboard is designed to demonstrate all func- tions for operating a complete LISA-like metrology system, to meet all performance requirements for a future mission and to study the effort of bringing the design to space qualification. Here we will present a system overview and the current status of testing and development of the bread- board. This includes phase readout of signals between 2 and 25 MHz with 1 microcycle/sqrt(Hz) per- formance, clock noise transfer, inter-satellite ranging and communication, laser frequency control and acquisition. In addition we present an optical non-linearity test, using three almost independent lasers, that we use to validate the performance of the full metrology chain by aiming to demonstrate the for LISA necessary dynamic range of 10 orders of magnitude at low frequencies.

181 Lisa experience from grace-fo optical payload

Francis S, Sutton A, Shaddock D, McKenzie K, Spero R, Ware B, Klipstein W

The LISA Experience from GRACE-FO Optical Payload (LEGOP) project aims to identify core-techniques and high-risk elements of LISA technology for testing upon the upcoming Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission. GRACE-FO will place two satellites into a common Low Earth Orbit separated by 200 km. By monitoring fluctuations in the inter-satellite distance, GRACE-FO measures the changes in Earth’s gravitational potential that occurs from mass and water transportation upon the Earth’s surface. In addition to the baseline microwave ranging system, GRACE-FO will carry a laser technology demonstrator, the Laser Ranging Instrument (LRI). The LRI will measure range across an inter-spacecraft laser link using heterodyne interferometry. This LRI shares many similarities with LISA including laser pre-stabilisation, Doppler shifts, 100 pW receive power and phase measurement based upon a digital phase-locked loop. LEGOP aims to exploit these similarities to demonstrate two technologies: Time Delay Interferometry (TDI), and Arm Locking. TDI represents the core measurement and top interferometry risk for LISA. Similarly, verification of Arm Locking will allow relaxation and simplification of laser stabilisation systems. As neither TDI nor Arm Locking can be fully represented on Earth, demonstrating their operation using the GRACE-FO optical link will advance the technology maturity and retire significant risk for future missions.

Decigo and decigo pathfinder

Akutsu T

DECIGO, DECi-hertz Interferometer Gravitational wave Observatory, is a space-based antenna planned to launch in the 2020s, and will observe gravitational-wave sources at low frequencies around 0.1Hz. Since this spectral region is not covered by the other planned gravitational wave antennas, DECIGO will provide new or complementary information to open a new window in science, including cosmology, astrophysics, and gravitation. In the current pre-conceptual design, DECIGO comprises four interferometer units. Each unit is formed by three drag-free spacecrafts with 1000-km separation, and the displacement of the spacecrafts will be precisely measured by a Fabry-Perot cavity. DECIGO Pathfinder (DPF) is the first milestone mission for DECIGO. Since DECIGO is an extremely challenging mission, it is important to increase the technical feasibility before its launch. DPF will be a single spacecraft launched to the low earth orbit in the middle of the 2010s, to test the key technologies and to carry out observation runs. In this talk, we will review the conceptual design and current status of DECIGO and DPF.

182 Poster session

Astrod-gw: overview and progress

Ni W

In this paper, we present an overview of Astrodynamical Space Test of Relativity using Optical Devices (ASTROD-GW) optimized for Gravitational Wave (GW) detection mission concept and its studies. ASTROD-GW is an optimization of ASTROD which focuses on low frequency GW detection. The detection sensitivity is shifted by a factor of 260 (52) towards longer wavelengths compared with that of NGO/eLISA (LISA). The mission consists of three spacecraft, each of which orbits near one of the Sun-Earth Lagrange points (L3, L4 and L5), such that the array forms an almost equilateral triangle. The three spacecraft range interferometrically with one another with an arm length of about 260 million kilometers. The orbits have been optimized resulting in arm length changes of less than 0.00015 AU or, fractionally, less than 10( − 4) in 20 years, and relative Doppler velocities of the three spacecraft of less than 3m/s. we present an overview of the mission covering: the scientific aims, the sensitivity spectrum, the basic orbit configuration, the simulation and optimization of the spacecraft orbits, the deployment of ASTROD-GW formation, Time Delay Interferometry (TDI) and the payload. A brief discussion of the six spacecraft orbit optimization is also presented.

Lisa technology package diagnostics during in-space conditions test campaign

Gibert F

The LISA Technology Package experiment (LTP) on board the LISA Pathfinder mission underwent a series of tests late in 2011 where the LTP Diagnostics Subsystem (DS) was tested for the first time in space conditions after integration to the satellite, following a series of characterisation thermal experiments. The DS will provide in flight key information regarding the thermal and magnetic field stability together with monitoring of charged particles. The LTP environment must be kept at a temperature and magnetic stability of 100uK/root(Hz) and 100nT/root(Hz) respectively, in the LTP measuring frequency band from 1mHz to 30mHz. This will ensure that the LTP differential acceleration requirement of 3 × 10−14m/s2/sqrt(Hz) is not affected from such perturbations. Here we report the main results from the DS during the campaign.

Parameter estimation in lisa pathfinder sensitive axis

Karnesis N

The LISA Pathfinder (LPF) mission will test key technologies for future space-borne Gravitational Wave missions like eLISA. Its main goal is to estimate the acceleration noise models of the overall LISA Technology Package (LTP) experiment on-board LPF. For this purpose, a series of system identification experiments have been proposed and each one is designed to provide with essential information about the system. Here, we present a study on those experiments based on the already developed statistical tools and techniques of the LTP Data Analysis (LTPDA) team. In particular, we focus on the sensitive axis of the experiment and we report on the predicted accuracy of the parameters that describe the system. We analyze each experiment separately using synthetic data produced by the LTPDA Matlab toolbox simulator.

183 Measurement of magnetic field at test masses in elisa/ngo

Mateos I , et A

The LISA Pathfinder experience indicates that magnetic field estimation at the TM’s positions have certain complications due to two basic facts: 1) magnetometers usually back act due to their measurement principles (i.e., these instruments also create magnetic fields themselves), and 2) sensors of large size conflict with space resolution and with the possibility of having a sufficient number of them to properly map the magnetic field around the TMs. We have been investigating high sensitivity and small size sensors which will significantly mitigate the two mentioned limitations, and which will therefore be suitable for magnetic diagnostics in eLISA/NGO. In this study we will address the quantitative analysis of the new set performance, as currently conceived.

A test-bed for lisa gravitational reference sensor characterization and charge control

Conklin J , Chilton A, Ciani G, Mueller G, Shelley R

LISA consists of three Sun-orbiting spacecraft that form a million km-scale equilateral triangle. Each spacecraft houses two free-floating test masses (TM), which are protected from disturbing forces so that they follow pure geodesics in spacetime. A single test mass together with its housing and associated components is referred to as a gravitational reference sensor (GRS). Laser interferometry is used to measure the minute variations in the distance between these free-falling TMs, caused by gravitational waves. The demanding acceleration noise requirement of 3 × 10−15m/sec2Hz1/2 for the LISA GRS has motivated various research activities at the University of Florida (UF). The first is the development of a nearly thermally noise limited torsion pendulum for testing the GRS and for understanding the dozens of acceleration noise sources that affect the performance of the LISA GRS. This experimental facility is based on the design of a similar facility at the University of Trento, and will consist of a vacuum enclosed torsion pendulum that suspends mock-ups of the LISA test masses, surrounded by electrode housings. The team at UF also collaborates with Stanford and the NASA Ames Research Center on a small satellite mission that will test the performance of UV LEDs for ac charge control in space. UV LEDs offer a lower cost method of maintaining the TM-to-spacecraft potential difference at the required level of 107 e, relative to the dc approach using traditional Hg lamps.

Status and perspectives of the two dof torsion pendulum facility peter

Bassan M, De Marchi F, De Rosa R, Di Fiore L, Garufi F, Grado A, Marconi L, Milano L, Pucacco G, Stanga R, Stolzi F, Visco M

PETER is a double torsion pendulum conceived for ground testing of the gravitational reference sensor (GRS) of LISA-like experiments with a test mass (TM) in free fall on two degrees of freedom. It is composed of a cross shaped first stage suspended in its center and a second stage with the GRS TM suspended at the end of one of the cross arms. In this way the pendulum has two soft degrees of freedom and allows us to measure at the same time both force and torque acting on the TM. The full structure is kept under high vacuum in order to reduce the environmental noise. The facility was designed, implemented and commissioned in the Florence INFN lab and has been extensively tested during the last two years. In this communication, we describe the apparatus, report on the measurements performed so far and discuss the preliminary results. The instrument will soon be transferred to the Napoli INFN lab where it will be placed on an independent concrete foundation in order to improve isolation from noise generated by human activity in the building. It will also be thermally isolated in order to reduce the low frequency noise. The expected performance improvement is presented and the perspective for the use of the facility for the ground testing of LISA-like flight hardware is discussed.

184 Experimental investigation of electrostatic dissipation on the motion of conducting test bodies

Cavalleri A, Dolesi R, Hueller M, Giuliana R, Tu H , Vitale S, Weber W, Wen S

For the motion of conducting test bodies, like the test mass in the gravitational reference sensors en- visioned to be used for space-borne gravitational wave detection like LISA mission and the torsion pendulums being used for high accurate gravitational experiments, the electrostatic dissipation arising from the surrounding conducting surfaces has been considered as one of important noise sources. In the article, we report two measurement techniques developed to quantitatively investigate the electrostatic dissipation, and the measurement results obtained with a high-precision torsion pendulum facility. For the gravitational reference sensor in LISA pathfinder design, the loss angle for a 4 mm capacitive gap −7 was measured to be deltaes = 3 × 10 with an uncertainty within 10%, for the Au-coated surfaces on the sensitive axis, which is well below the LISA budget. A few additional tests have also been performed to study the properties of the surface dissipation, as well as the ohmic losses due to the low-pass filtering effect existing in the servo circuitry.

Measuring test mass acceleration noise in lisa pathfinder

Congedo G

LISA Pathfinder will be the first implementation in space of a single arm of future low-frequency gravita- tional wave detectors. Besides the characterization of key technologies (e.g., drag-free control, thrusters and gravitational reference systems), the top-priority goal will be the measurement of the acceleration noise affecting the relative motion of two free-falling test masses, at distance less than a meter. It is well know that everything not accountable as gravity curvature or inertial effects is a source of deviation from the geodesic motion. Particularly below 1 mHz, the test mass is affected by coupling forces with the local environment in the spacecraft. The accurate measurement of the acceleration noise relies upon estimating the parameters which model various non-idealities in the system. Also, control forces are continually applied to the system: as such, they must be subtracted from the observed motion with the right synchronization. We make a change of viewpoint by describing the system not at the level of outputs (displacements), but inputs (accelerations). The new devised method described here merges the measurement of the acceleration noise with parameter estimation. Two benefits are the followings: (i) better performances achieved at lower frequencies, compared to as previous analysis; (ii) nominal suppression of the system’s free evolution due to non-null initial conditions, an unavoidable affect in the slow dynamics of low-frequency detectors.

Experimental characterisation of tilt-to-length coupling on the lisa optical bench

Troebs M

The measurements of distance changes within the Laser Interferometer Space Antenna (LISA) will be carried out on optical benches. One interferometer (test mass interferometer) measures the distance changes between test mass and optical bench, another interferometer (science interferometer) measures distance changes between local and remote optical bench. Tilts of test mass or spacecraft couple into the interferometric length measurement. We report on the current status of a dedicated experiment that investigates the resulting tilt-to-length coupling and concentrates on the science interferometer. Here, the flat-top beam from the remote space- craft is interfered with a Gaussian local oscillator. The optical bench contains the science interferometer

185 with two redundant photo detectors and imaging systems that shall reduce the tilt-to-length coupling to below 20 pm/urad. A special test equipment called telescope simulator creates and tilts a flat-top beam as it would be received from the remote satellite. Two techniques to decouple the tilt-to-length coupling caused by telescope simulator and optical bench will be investigated experimentally.

Tilt to pathlength readout coupling: noise predictions and mitigation in various projects

Wanner G, Dahl K, Mahrdt C, Kochkina E, Schuster S, Sch¨utzeD, Tr¨obsM, Heinzel G, Danzmann K

Cross coupling of angular beam jitter into pathlength readout is a strong effect in many interferometers, like for instance in LISA, LISA Pathfinder, GRACE follow on, but also for instance in the suspension platform interferometer (SPI) of the AEI 10m prototype. We will present pathlength noise estimates caused by angular jitter. Additionally, we will present methods currently available to reduce this effect - imaging optics, use of single element photo diodes, noise subtraction and active stabilization - and discuss their limitations.

Lisa pathfinder: optical metrology system noise characterisation, and the associated in-flight experiments

Audley H

The LISA Pathfinder (LPF) mission aims to demonstrate some of the key technologies required for a future LISA-type (Laser Interferometer Space Antenna) gravitational wave interferometer. Specifically, the control of drag-free masses using high-precision interferometry and micro-Newton thrusters. At the core of the LPF satellite is the Optical Metrology System (OMS), the interferometric measurement system for the position and orientation of the drag-free test masses. Ground-based testing of the Flight Model OMS has been performed, both at system level, and after integration with other subsystems into the satellite body. The data collected in these tests not only demonstrates that the OMS functions as required, but provides a wealth of information that is essential for further system characterisation and, importantly, for the preparation of in-flight experiments and the associated analyses. This contribution will report on the results of the characterisation analyses, highlighting the differences between the setups under test and the expected extrapolation to the in-flight configuration. In addition, the data analysis methods developed during these analyses and their relevance to the planned in-flight experiments will be discussed.

Study of photoreceivers for space-based interferometry

Fernandez Barranco G, Diekmann C, Tr¨obsM, Heinzel G, Danzmann K

The photoreceiver is a basic element in laser interferometry systems presented in space-based missions such as Lisa Pathfinder or GRACE Follow-On. The special requirements demanded by those systems rule out any commercial solution for the photoreceiver. Therefore, new photoreceiver designs have been developed and characterized in the institute, focusing the efforts on the bandwidth, noise performance and phase stability. Additionally, a spatial characterization system was configured to perform scans of the photodiodes’ surface, which allow a real understanding of the response of those devices.

186 Back-link for the lisa optical bench

Lieser M , Bogenstahl J, Diekmann C, Henning J, Tr¨obsM, Heinzel G, Danzmann K

The optical bench is the main optical instrument of a laser interferometer space antenna (LISA) mission. It is an ultra-stable Zerodur baseplate with several bonded interferometers. The distance measurements for the gravitational wave observation will be done on the optical bench. In the actual baseline design there are two optical benches per spacecraft - one behind each telescope. The telescopes are movable to point to the distant spacecraft and the optical benches are moving with the telescopes. Between the measurements in the two interferometer arms a phase reference has to be delivered to the other bench via a flexible reciprocal connection. A previous experiment with a fiber- based backlink has shown a good reciprocity of the fiber but only by elimination of stray light effects in post processing. Here we present an ongoing experiment to investigate one of the possible solutions to suppress stray light in the measurement that is to attenuate the beams behind the fiber couplers.

Measuring small acceleration fluctuations in the presence of a large dc acceleration: a torsion pendulum test

Dolesi R, Hueller M, Russano G, Tu H, Vitale S, Weber W , Wen S, Cavalleri A

Many gravitational experiments in orbit require detection of small, time varying accelerations of a test particle in the presence of a much larger, effectively constant acceleration that must be actively compen- sated in order to keep the test particle centered inside an orbiting apparatus. This active compensation by force actuation introduces force noise, which, in the case of geodesy missions or the LISA Pathfinder geodesic explorer mission for gravitational wave astronomy, can be the dominant noise source. In LISA Pathfinder, a ”free-fall” control scheme has been proposed in which the force actuation is limited to brief impulses separated by longer periods in which the actuator is turned off, allowing intervals of data with a free-falling test mass, without the added noise of the actuator. In this poster, we will propose an on-ground torsion pendulum experiment to test this technique, and the associated analysis algorithms, at a level nearing the sub-femto-g/sqrt(Hz) performance required for LISA Pathfinder.

Choosing the initial lisa orbital configuration

Benacquista M , Finn L, Jani K

Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three spacecraft in a special set of drag-free heliocentric orbits. Once these spacecraft are placed in their orbits, the orientation of the interferometers at any future time is fixed by Kepler’s Laws based on the initial orientation of the spacecraft constellation. Over the course of a full solar orbit, the initial orientation determines those locations in the sky were the detector has greatest sensitivity to gravitational waves as well as those locations where nulls in the detector response fall. By artful choice of the initial orientation, we can choose to optimize sensitivity to sources whose location may be known in advance (e.g., the Galactic center or globular clusters).

187 Approaching the lisa performance with the lpf free-flight experiment

Hewitson M

The LISA Pathfinder (LPF) mission will demonstrate key technologies for future space-borne gravita- tional wave observatories, like LISA. Due to its configuration, LPF has an additional noise source which will not be present in a LISA-like mission. This noise source arises from the fact that LPF has two co-linear test-masses, one which is free-falling, and one which serves as a quiet witness of the motion of the first. The second test-mass is necessarily controlled to follow the larger below band motion of the first. This introduces an actuation noise term in the total error budget which is not present in LISA-like configurations To explore this noise source, and to probe below it, an experiment has been designed on LPF in which the actuation of the 2nd test mass is turned off, placing both test masses in free-fall for a few minutes. The actuation is then briefly restored to return the 2nd test mass to its nominal position, before being turned off again. This process is repeated many times, and the subsequent data is analysed to estimate the residual differential acceleration on time-scales much longer than the drift phases. Doing so may allow us to expose the contribution from spurious test-mass forces. This talk will describe the experiment, and discuss methods by which the data can be analysed, con- cluding with predictions for the sensitivity of LPF in the context of LISA-like instruments, showing an expected performance well below the mission goal.

Kolmogorov-smirnov test for time-frequency fourier spectrogram analysis

Ferraioli L

A statistical procedure for the analysis of time-frequency noise maps is presented and applied to LISA Pathfinder mission synthetic data. Such procedure is based on the Kolmogorov-Smirnov test that is applied to the analysis of time-frequency noise maps produced with the spectrogram technique. The presented method can be used for the implementation of a noise monitoring pipeline for LISA Pathfinder data. The influence of the finite size data windowing on the statistic of the test is calculated with a Monte Carlo simulation for 4 different data windows. Such calculation demonstrates that the test statistic is affected by the correlation introduced in the spectrum by the finite size of the window and the correlation between different time bins originated by the overlapping between windowed segments. The application of the test procedure to LISA Pathfinder data demonstrates the test capability of detecting non-stationary features in a noise time series. As an example we report a noise data series that simulates non-stationary noise in the capacitive actuation system.

Optimal calibration signals for lisa pathfinder test mass dynamics

Nofrarias M

LISA Pathfinder (LPF) is an ESA mission with NASA contributions designed to test key technologies for the detection of gravitational waves in space. The main scientific goal of the mission is expressed as a differential acceleration noise between two test masses in nominal free-fall of 3 × 10−14m/s2/sqrt(Hz) in the millihertz band. In order to achieve this highly sensitive measurement, the instrument will undergo a sequence of experiments during the six months duration of the mission. These planned experiments are designed to allow a precise determination of the parameters defining the noise model of the system, a key information for the forthcoming space-borne gravitational wave observatories. Given the short duration of the mission and the typical time constraints arising from a 8 hours daily communication window with the satellite, the optimisation of the scientific yield in terms of achieved precision and

188 required measurement time is crucial. In this contribution we propose an approach to cope with this problem based on the experiment design theory: we apply an algorithm which looks for the optimal calibration input signals in the sense that it guarantees a minimum uncertainty in the determination of the instrument parameters for a given measurement time. In this contribution we present the results when applied to the optimisation of the input signals to calibrate the LPF test mass dynamics.

The data analysis of gapped data series

Vetrugno D

LISA Pathfinder (LPF) is an in-flight technological demonstrator who aims to show the capability of high precision metrology between two free-falling objects in space. In practice, it consists of a series of experiments designed to test the instrument and the needed requirements. During the mission, our data could be characterised by the presence of gaps. This is also a very common situation in astrophysics. In the case of LPF, we can imagine at least three different ways to have gapped data. Firstly, the data we will get from the satellite may have gaps of a few seconds in it and we need of a method to cope with such gaps. Secondly, data could have large glitches and we must reject these data. Eventually, in the case of performing the Free-Flight Experiment, data coming out from it are naturally characterized by gaps. Indeed, because of the presence of stretches of data ten times noisier than the free falling data, we have to reject the former. In all these cases, the noise spectrum will be corrupted by the convolution with rectangular windows. Different techniques have been developed for dealing with this type of data, depending on whether the data are evenly or unevenly sampled. The technique can also depend on the duration of gaps. We present here different results with different techniques and make the point on the ”state of the arts” of this type of analysis.

189 C6 - Q&A Everything you wanted to know about GWs but were afraid to ask

Oral session

Why do we believe that GWs exist?

Cornish N

What kinds of supernovae could produce a detectable GW signal?

Reisswig C

How does searching for gravitational waves help us here on Earth?

Stuver A

What will be the first source detected by LIGO-Virgo?

Broeck C

Do laser interferometer gravitational wave detectors absorb energy from gravitational waves?

Sturani R

190 Why is it possible to achieve a higher signal-to-noise ratio by holding a GW interferometer’s signal port at the dark fringe as opposed to halfway up a fringe?

Barsotti L

When do we finally get to make the first detection?

Sutton P

191 C7 - Multi-Messenger Astronomy of GW Sources

Oral session

Grb beaming and gravitational-wave observations

Holz D, Chen H

Using the observed rate of short-duration gamma-ray bursts (GRBs) it is possible to make predictions for the detectable rate of compact binary coalescences in gravitational-wave detectors. We make predictions for the rate of events in future networks of gravitational-wave observatories, finding that the first detection of a NS–NS binary coalescence associated with the progenitors of short GRBs is likely to happen within the first 16 months of observation, even in the case of only two observatories (e.g., LIGO-Hanford and LIGO-Livingston) operating at intermediate sensitivities (e.g., advanced LIGO design sensitivity, but without signal recycling mirrors), and assuming a conservative distribution of beaming angles (e.g. all GRBs beamed within 30 deg). Less conservative assumptions reduce the waiting time to a period of weeks to months. Alternatively, the compact binary coalescence model of short GRBs can be ruled out if a binary is not seen within two years by a three detector network at advanced design sensitivity. We demonstrate that the gravitational wave detection rate of GRB triggered sources (i.e., those seen first in gamma rays) is lower than the rate of untriggered events (i.e., those seen only in gravitational waves) if the beaming is less than 30 deg, independent of the noise curve, network configuration, and observed GRB rate. The first detection in gravitational waves of a binary GRB progenitor is therefore unlikely to be associated with the observation of a GRB.

Follow-up activities for the transient universe

Covino S

Variable and transient objects encompass all astronomical distances ranging from comets and asteroids, stars (normal and compact), novae, supernovae, blazars, tidal disruption events and gamma-ray bursts (GRBs). Still time domain astronomy is in its infancy. Now the first surveys start probing the transient sky especially at optical (Palomar Transient Factory, PTF; PanSTARRS, and in the future the Large Synoptic Survey Telescope, LSST) and radio (Low Frequency ARray, LOFAR, and later on the Square Kilometer Array, SKA) wavelengths. The discovery space in this field is immense. The search for electromagnetic counterparts for gravitational wave (GW) astronomy is clearly part of this growing importance and exciting field.

192 However, the management of large scale follow-up activities is never an easy task, and many subtle issues have to be properly handled. The author has been directly involved in the organization, design and management of the Italian follow-up activities for GRBs since the launch of the Swift satellite. Some considerations based on this experience can be offered to the GW community now that the epoch of the first meaningful GW scientific observations and hopefully first candidate detections is getting closer and closer.

Use of galaxy catalogs for following up gw detections from binary neutron star mergers using advanced detectors

Vousden W , Hanna C, Mandel I

The 10 − 100deg2 localization error provided by gravitational wave transient searches presents a chal- lenging problem for astronomers hoping to promptly follow up gravitational wave observations of binary neutron star mergers with electromagnetic instruments. It has been suggested that restricting obser- vations to known galaxies within the search range may significantly reduce the area of sky that must be imaged; however, current and proposed follow-up surveys can take wide-field images with FOV of 0.1 − 10deg2, and in this scenario we can expect many galaxies per field of view. We assess the utility of a galaxy catalog in directing such an EM follow-up in terms of two parameters: the mean number of galaxies per field-of-view, and the fractional coverage of the search area available with limited telescope time. While still challenging, we show that the inherent fluctuations in the galaxy number per pointing do modestly improve the prospects of follow-up for some wide-field surveys.

Young dense star clusters: the nursery of double compact-object binaries

Mapelli M , Ziosi B

Young dense star clusters (SCs) are the nursery of stars: about 80% of stars are expected to form in SCs. Furthermore, SCs are dynamically active sites: binary systems continuously form, evolve and destroy in SCs because of dynamical interactions. This has dramatic consequences for compact objects (COs), such as stellar-mass black holes (BHs) and neutron stars (NSs): a CO that was born as a single object in a dense SC can become member of a binary after a dynamical exchange. In this talk, I discuss the results of innovative N-body simulations, which investigate the dynamical formation of double CO binaries in SCs. These simulations include recipes for metal-dependent stellar evolution, stellar winds and formation of stellar remnants. I show that the joint effect of dynamics and metallicity-dependent remnant formation can significantly boost the formation of BH-BH binaries, making them the most common class of double CO binaries in SCs. Furthermore, I show that the formation rate of BH-NS binaries is enhanced with respect to the formation rate of NS-NS binaries, at low metallicity. These results have important consequences for the electromagnetic (EM) counterparts of double CO binaries. I speculate about the most relevant consequences for gravitational wave (GW) emission by merging CO binaries, in light of the forthcoming 2nd-generation ground-based GW detectors. The talk will underline the importance of EM/GW observations to constrain different physical scenarios.

Measuring the masses of white dwarf binaries - a multimessenger approach

Johnson-McDaniel N , Koop M, Langdon H, Lundberg A, Finn L

We show how one can combine together gravitational wave measurements of white dwarf binaries with standard electromagnetic observations to measure the masses of the binaries’ components. We then

193 evaluate the anticipated accuracy of this measurement for the binaries in a population synthesis model of the galaxy. In one possible scenario (using the parallax from Gaia and the mass function from spectroscopy), we find that one can measure the masses of hundreds of systems with accuracies of tens of percent, using classic LISA. We also consider NGO/eLISA with 1 Gm and 2 Gm arms and evaluate the properties of the subpopulation with accurate mass measurements for each of these detectors. The number of systems with accurate mass measurements decreases as the detector’s sensitivity decreases, but even for NGO/eLISA with 1 Gm arms, one can still measure the masses of 100 systems with accuracies of a few percent.

G2 can illuminate the black hole population near the galactic center

Bartos I

Galactic nuclei are expected to be densely populated with stellar and intermediate mass black holes. Exploring this population will have important consequences for the observation prospects of gravitational waves as well as understanding galactic evolution. The gas cloud G2 currently approaching Sgr A* provides an unprecedented opportunity to probe the black hole and neutron star population of the Galactic nucleus. We examine the possibility of a G2-black hole encounter and its detectability with current X-ray satellites, such as Chandra and NuSTAR. We find that multiple encounters are likely to occur close to the pericenter, which may be detectable upon favorable circumstances. This opportunity provides an additional, important science case for leading X-ray observatories to closely follow G2 on its way to the nucleus.

Astronomical guidance for directed searches for continuous gravitational waves

Owen B

The LIGO Scientific Collaboration and Virgo Collaboration have published a search for continuous gravitational-waves from the non-pulsing neutron star in supernova remnant Cas A. More such searches, where the direction is known but no pulsar timing is available, are under way. I describe the astronomical criteria for good targets for such gravitational-wave searches, list classes of astronomical objects, and give examples of each class.

An update on magnetic mountains as advanced ligo sources

Melatos A

The spin frequency distribution of neutron stars in low-mass X-ray binaries (LMXBs) exhibits a sharp cut-off well below the centrifugal breakup limit. If the cut-off is interpreted in terms of gravitational- wave stalling, LMXBs should emit a relatively strong, periodic gravitational wave signal detectable by Advanced LIGO. One natural way to create the necessary nonaxisymmetry is to build up a mountain by funneling accreting gas magnetically onto the poles of the star. In this talk, I present the latest results from theoretical modelling of magnetic mountains. These include: equilibrium states in 2D and 3D and their hydromagnetic stability, the role of resistive relaxation and sinking, global oscillations of the mountain, and the effect of the nuclear equation of state. Already, non-detections with Initial LIGO place interesting upper limits on the electrical resistivity of neutron star matter. I also report on the status of a sideband search for Scorpius X-1, the brightest LMXB. Multi-messenger experiments are proposed which aim to distinguish between magnetic mountains and quadrupoles of other sorts in the

194 event of an Advanced LIGO detection, e.g. by making connections with electromagnetic phenomena like the spin down of the accreting millisecond pulsar J1808-3658, the evidence for ”patchy” nuclear burning in thermonuclear X-ray bursts, the spectra of X-ray cyclotron lines, and the radio polarisation swing in millisecond pulsars.

The r-mode instability and the interior physics of neutron stars: constraints from x-ray, uv and gw signals

Haskell B

Rapidly rotating neutron stars in low-mass X-ray binaries may be an interesting source of gravitational waves (GWs). In particular, several modes of stellar oscillation may be driven unstable by GW emission, and this can lead to a signal that may be detectable by next generation GW detectors. I will discuss this scenario in detail and illustrate how current X-ray and ultraviolet observations can constrain the physics of the r-mode instability. In particular I will show that the core temperatures inferred from the data would place many systems well inside the unstable region predicted by standard physical models. However, this is at odds with theoretical expectations. I will discuss different mechanisms that could be at work in the stellar interior, and show how they can modify the instability window and make it consistent with the inferred temperatures. Finally I will discuss how superfluidity in the neutron star interior can affect the maximum amplitude of the unstable mode and affect the GW emission.

Neutron star oscillations from starquakes

Keer L, Jones I

Glitches - sudden increases in spin rate - are observed in many pulsars. One mechanism that has been proposed to account for these glitches is the starquake model, in which they are triggered by a sudden loss of strain from the solid crust of the star. Starquakes can be expected to excite oscillation modes of the neutron star. These oscillations are of interest both as a source of gravitational waves and as a radio source. We describe a model that we are developing to calculate changes in the properties of the star during a starquake, in order to work out how it oscillates after the glitch.

Limiting bimetric theories of gravity and massive gravity theories with multi-messenger astronomy of pulsars

Hazboun J , Larson S

Recent work has reinvigorated the study of bimetric theories of gravity and massive gravity theories. One of the most interesting predictions of these theories is the subluminal speed of propagating gravitational waves. Multi-messenger astronomy provides a unique opportunity in the case of pulsars to put limits on the difference between the propagation speed of electromagnetic and gravitational waves from these sources. The LIGO collaboration has put limits on gravitational wave emission from a large number of pulsars, all of which are routinely optically observed. Comparing the phases of the two types of signal allows limits to be put on the difference of the gravitational wave speed from that of light, and on the mass of the graviton. Observations of the pulsars in the most sensitive range of LIGO could put an upper limit on the graviton mass as low as 10E-21 eV and an upper limit on the difference between the waves speeds as low as 10E-10.

195 Poster session

Neutron star oscillations from starquakes

Keer L, Jones I

Glitches - sudden increases in spin rate - are observed in many pulsars. One mechanism that has been proposed to account for these glitches is the starquake model, in which they are triggered by a sudden loss of strain from the solid crust of the star. Starquakes can be expected to excite oscillation modes of the neutron star. These oscillations are of interest both as a source of gravitational waves and as a radio source. We describe a model that we are developing to calculate changes in the properties of the star during a starquake, in order to work out how it oscillates after the glitch.

Limiting bimetric theories of gravity and massive gravity theories with multi-messenger astronomy of pulsars

Hazboun J , Larson S

Recent work has reinvigorated the study of bimetric theories of gravity and massive gravity theories. One of the most interesting predictions of these theories is the subluminal speed of propagating gravitational waves. Multi-messenger astronomy provides a unique opportunity in the case of pulsars to put limits on the difference between the propagation speed of electromagnetic and gravitational waves from these sources. The LIGO collaboration has put limits on gravitational wave emission from a large number of pulsars, all of which are routinely optically observed. Comparing the phases of the two types of signal allows limits to be put on the difference of the gravitational wave speed from that of light, and on the mass of the graviton. Observations of the pulsars in the most sensitive range of LIGO could put an upper limit on the graviton mass as low as 10E-21 eV and an upper limit on the difference between the waves speeds as low as 10E-10.

An update on magnetic mountains as advanced ligo sources

Melatos A

The spin frequency distribution of neutron stars in low-mass X-ray binaries (LMXBs) exhibits a sharp cut-off well below the centrifugal breakup limit. If the cut-off is interpreted in terms of gravitational- wave stalling, LMXBs should emit a relatively strong, periodic gravitational wave signal detectable by Advanced LIGO. One natural way to create the necessary nonaxisymmetry is to build up a mountain by funneling accreting gas magnetically onto the poles of the star. In this talk, I present the latest results from theoretical modelling of magnetic mountains. These include: equilibrium states in 2D and 3D and their hydromagnetic stability, the role of resistive relaxation and sinking, global oscillations of the mountain, and the effect of the nuclear equation of state. Already, non-detections with Initial LIGO place interesting upper limits on the electrical resistivity of neutron star matter. I also report on the status of a sideband search for Scorpius X-1, the brightest LMXB. Multi-messenger experiments are proposed which aim to distinguish between magnetic mountains and quadrupoles of other sorts in the event of an Advanced LIGO detection, e.g. by making connections with electromagnetic phenomena like the spin down of the accreting millisecond pulsar J1808-3658, the evidence for ”patchy” nuclear burning in thermonuclear X-ray bursts, the spectra of X-ray cyclotron lines, and the radio polarisation swing in millisecond pulsars.

196 Measuring the masses of white dwarf binaries - a multimessenger approach

Johnson-McDaniel N , Koop M, Langdon H, Lundberg A, Finn L

We show how one can combine together gravitational wave measurements of white dwarf binaries with standard electromagnetic observations to measure the masses of the binaries’ components. We then evaluate the anticipated accuracy of this measurement for the binaries in a population synthesis model of the galaxy. In one possible scenario (using the parallax from Gaia and the mass function from spectroscopy), we find that one can measure the masses of hundreds of systems with accuracies of tens of percent, using classic LISA. We also consider NGO/eLISA with 1 Gm and 2 Gm arms and evaluate the properties of the subpopulation with accurate mass measurements for each of these detectors. The number of systems with accurate mass measurements decreases as the detector’s sensitivity decreases, but even for NGO/eLISA with 1 Gm arms, one can still measure the masses of 100 systems with accuracies of a few percent.

Use of galaxy catalogs for following up gw detections from binary neutron star mergers using advanced detectors

Vousden W , Hanna C, Mandel I

The 10 − 100 deg2 localization error provided by gravitational wave transient searches presents a chal- lenging problem for astronomers hoping to promptly follow up gravitational wave observations of binary neutron star mergers with electromagnetic instruments. It has been suggested that restricting obser- vations to known galaxies within the search range may significantly reduce the area of sky that must be imaged; however, current and proposed follow-up surveys can take wide-field images with FOV of 0.1 − 10 deg2, and in this scenario we can expect many galaxies per field of view. We assess the utility of a galaxy catalog in directing such an EM follow-up in terms of two parameters: the mean number of galaxies per field-of-view, and the fractional coverage of the search area available with limited telescope time. While still challenging, we show that the inherent fluctuations in the galaxy number per pointing do modestly improve the prospects of follow-up for some wide-field surveys.

The r-mode instability and the interior physics of neutron stars: constraints from x-ray, uv and gw signals

Haskell B

Rapidly rotating neutron stars in low-mass X-ray binaries may be an interesting source of gravitational waves (GWs). In particular, several modes of stellar oscillation may be driven unstable by GW emission, and this can lead to a signal that may be detectable by next generation GW detectors. I will discuss this scenario in detail and illustrate how current X-ray and ultraviolet observations can constrain the physics of the r-mode instability. In particular I will show that the core temperatures inferred from the data would place many systems well inside the unstable region predicted by standard physical models. However, this is at odds with theoretical expectations. I will discuss different mechanisms that could be at work in the stellar interior, and show how they can modify the instability window and make it consistent with the inferred temperatures. Finally I will discuss how superfluidity in the neutron star interior can affect the maximum amplitude of the unstable mode and affect the GW emission.

197 Grb beaming and gravitational-wave observations

Holz D, Chen H

Using the observed rate of short-duration gamma-ray bursts (GRBs) it is possible to make predictions for the detectable rate of compact binary coalescences in gravitational-wave detectors. We make predictions for the rate of events in future networks of gravitational-wave observatories, finding that the first detection of a NS–NS binary coalescence associated with the progenitors of short GRBs is likely to happen within the first 16 months of observation, even in the case of only two observatories (e.g., LIGO-Hanford and LIGO-Livingston) operating at intermediate sensitivities (e.g., advanced LIGO design sensitivity, but without signal recycling mirrors), and assuming a conservative distribution of beaming angles (e.g. all GRBs beamed within 30 deg). Less conservative assumptions reduce the waiting time to a period of weeks to months. Alternatively, the compact binary coalescence model of short GRBs can be ruled out if a binary is not seen within two years by a three detector network at advanced design sensitivity. We demonstrate that the gravitational wave detection rate of GRB triggered sources (i.e., those seen first in gamma rays) is lower than the rate of untriggered events (i.e., those seen only in gravitational waves) if the beaming is less than 30 deg, independent of the noise curve, network configuration, and observed GRB rate. The first detection in gravitational waves of a binary GRB progenitor is therefore unlikely to be associated with the observation of a GRB.

Young dense star clusters: the nursery of double compact-object binaries

Mapelli M , Ziosi B

Young dense star clusters (SCs) are the nursery of stars: about 80% of stars are expected to form in SCs. Furthermore, SCs are dynamically active sites: binary systems continuously form, evolve and destroy in SCs because of dynamical interactions. This has dramatic consequences for compact objects (COs), such as stellar-mass black holes (BHs) and neutron stars (NSs): a CO that was born as a single object in a dense SC can become member of a binary after a dynamical exchange. In this talk, I discuss the results of innovative N-body simulations, which investigate the dynamical formation of double CO binaries in SCs. These simulations include recipes for metal-dependent stellar evolution, stellar winds and formation of stellar remnants. I show that the joint effect of dynamics and metallicity-dependent remnant formation can significantly boost the formation of BH-BH binaries, making them the most common class of double CO binaries in SCs. Furthermore, I show that the formation rate of BH-NS binaries is enhanced with respect to the formation rate of NS-NS binaries, at low metallicity. These results have important consequences for the electromagnetic (EM) counterparts of double CO binaries. I speculate about the most relevant consequences for gravitational wave (GW) emission by merging CO binaries, in light of the forthcoming 2nd-generation ground-based GW detectors. The talk will underline the importance of EM/GW observations to constrain different physical scenarios.

Follow-up activities for the transient universe

Covino S

Variable and transient objects encompass all astronomical distances ranging from comets and asteroids, stars (normal and compact), novae, supernovae, blazars, tidal disruption events and gamma-ray bursts (GRBs). Still time domain astronomy is in its infancy. Now the first surveys start probing the transient sky especially at optical (Palomar Transient Factory, PTF; PanSTARRS, and in the future the Large Synoptic Survey Telescope, LSST) and radio (Low Frequency ARray, LOFAR, and later on the Square Kilometer Array, SKA) wavelengths. The discovery space in this field is immense.

198 The search for electromagnetic counterparts for gravitational wave (GW) astronomy is clearly part of this growing importance and exciting field. However, the management of large scale follow-up activities is never an easy task, and many subtle issues have to be properly handled. The author has been directly involved in the organization, design and management of the Italian follow-up activities for GRBs since the launch of the Swift satellite. Some considerations based on this experience can be offered to the GW community now that the epoch of the first meaningful GW scientific observations and hopefully first candidate detections is getting closer and closer.

Astronomical guidance for directed searches for continuous gravitational waves

Owen B

The LIGO Scientific Collaboration and Virgo Collaboration have published a search for continuous gravitational-waves from the non-pulsing neutron star in supernova remnant Cas A. More such searches, where the direction is known but no pulsar timing is available, are under way. I describe the astronomical criteria for good targets for such gravitational-wave searches, list classes of astronomical objects, and give examples of each class.

199 C8 - Education and Public Outreach on Gravitational Wave Astronomy

Oral session

Education and public outreach: skills and media

Stuver A

A primary requirement of scientific research is to disseminate results. While scientists primarily view the audience of their research to be scientific peers, it is the public (often a main source of funding) who has the most to gain from the application of this new knowledge. Therefore, it is also a responsibility of scientists to engage the public with active scientific research and researchers through education and outreach efforts. However, it can be difficult to find education and public outreach outlets that are appropriate to personal skills and availability. This presentation outlines the speaker’s experiences at the LIGO Science Education Center, co-located at the Livingston observatory, and lessons learned on how to engage students and the general public in person and through internet outlets. Various media one can use to engage the public in their research will be discussed as well as ways to interact respectfully with those whose worldview conflicts with their research.

Public outreach via social networks and more: elisa and the esa l2 mission selection

Gerberding O, Barke S, Audley H, Knispel B, Lieser M, Danzmann K

At the beginning of 2013 the Albert-Einstein Institute and its partners from the eLISA consortium started an outreach campaign for eLISA. The aim of this is to increase awareness of a space-based gravitational wave detector, and its associated science. This was considered particularly important to counteract the negative attention generated by the financial problems of NASA in 2011 and the non-selection of the European-only NGO-version of LISA for the ESA L1 launch slot in 2012. The campaign also aimed to generate attention and support for the L2/L3 mission call for science themes that required submission of a white paper before the 24th of May. The first major step was an exhibition during the spring meeting of the German Physical Society in March. In parallel, an online presence of the eLISA mission on all major social networks was initiated.

200 The first goal is to inform enthusiasts, fans, and scientists of new developments, findings, and useful information. The second is to reach out to people not-yet familiar with the eLISA mission concept, by providing content that was easily accessible, and that could engage a broad audience. We created several educational stop-motion drawing videos to allow easy access to our science, as well as ”internet memes” based on current media trends, reaching over two million people. Here we will give an overview of the campaign, present the current numbers of fans and activities on our sites, show a few examples of our content, and report on the required workload and organisation. Finally we will have an open discussion on the overall success.

Einstein first: changing the paradigm of physics teaching at school.

Blair D, Ron B, Marjan Z, Kaur T

Between 1900 and 1920 discoveries by Einstein and others revolutionised physics. The proof of existence of photons led to quantum mechanics while proof that space is curved confirmed the core prediction of Einstein’s general theory of relativity. Today the theories that we term Einsteinian physics have been tested to exquisite precision. They lead to a completely new understanding of space, time, gravity, matter and radiation. Almost 100 years later physics at school is still taught from an obsolete Newtonian standpoint, even though Einsteinian physics lies at the heart of modern technology such as mobile phones, as well as space science, astronomy and timekeeping. The discovery of gravitational waves will make it even more relevant. In this talk I will report a series of pilot studies that have investigated the ability of children aged 11-12 and 16 to comprehend physics taught from an Einsteinian standpoint. With colleagues we have developed curriculum material and teaching aids that bring Einsteinian physics vividly to life. Our results demonstrate that the concepts of Einsteinian physics are readily accepted by younger students, while older students believe that it would have been useful to have learnt the concepts at an earlier age. I will argue that we owe it to our children to teach them the Einsteinian reality that today represents our best understanding of the universe, while presenting Newtonian physics as a useful approximation.

Einstein@Home

Allen B

Einstein@Home is a volunteer distributed computing project. Volunteers from the general public partic- ipate by ”signing up” their laptop or desktop computers. When these are otherwise unoccupied, these computers automatically download astrophysical data from our project servers, and search it for the weak gravitational-wave or electromagnetic signals produced by spinning neutron stars. To date, Ein- stein@Home has discovered about fifty new pulsars, including a number of exotic and interesting systems. More than 350,000 members of the public, from all 192 countries recognized by the United Nations, have contributed.

201 Inspiring undergraduate interest: aspects of the nsf´sireu program

Whiting B

At a national level, the National Science Foundation (NSF) in the US is attempting to stem the tide of undergraduates turning irrevocably away from Physics before they have an opportunity to experience the excitement of research. Research Experiences for Undergraduates (REU) programs are designed to introduce students to research as early as possible so as to awaken, or sustain, an interest in a life dedicated to research. International REU (or IREU) programs go one step further, by exposing students to the international arena of research, awakening them to large-scale collaborative projects, and giving them an invaluable networking opportunity even before they enter graduate school. These programs entail dealing with many specific issues at both the organizational and host level. Understanding these issues, and developing creative ways to deal with them are crucial to the success of such programs. Ultimately, the maximum benefit for hosts also depends on a shrewd investment for success.

Teaching general relativity to undergraduates

Christensen N , Moore T

Inspired by new results in cosmology and astrophysics, undergraduates are increasingly eager to learn about general relativity. Undergraduates are participating in gravitational wave research around the world, and their desire to learn and understand general relativity is coupled to both their research and education goals. Those who teach general relativity to undergraduates can take advantage of a decade’s worth of pedagogical progress. Various educational techniques long used in teaching electrodynamics and quantum mechanics to undergraduates can now be successfully applied to general relativity, and new textbooks are making such approaches broadly accessible. General relativity is therefore rapidly becoming as important as many topics traditionally covered for an undergraduate physics degree. We strongly recommend that any major-granting department consider a regular course offering in this fasci- nating subject. Here we present some ideas and advice in order to help make effective teaching of general relativity to undergraduates a reality.

Big waves: a different kind of gravitational-wave summer school

Mandel I , Freise A, Vecchio A

In the summer of 2012, we organized a Birmingham Gravitational-wave summer school (BiG Waves) with an unusual format that focused on active student involvement. In lieu of lectures, students read ten keys papers from the fields of gravitational-wave instrumentation, data analysis, and astrophysics in advance of the school, and then analyzed them during the school in the format of shotgun seminars. Students also engaged in two hands-on projects. On the experimental side, participants had the opportunity to build and program a stand-alone voice-recognition system. On the data analysis side, participants implemented an optimal matched filtering search and a Markov Chain Monte Carlo parameter estimation analysis on mock data. We report on the successful features of the school as well as on opportunities for further improvement of this hands-on model.

202 Poster session

Reconstructing the sky position of coalescing binaries from gravitational-wave data using bayesian methods

Sidery T

When the next generation of gravitational-wave interferometers come online we expect to follow up detections of coalescing compact binaries with electromagnetic observations. Accurate sky locations will be needed to help point these follow up searches. A number of codes based on Bayesian analysis have been developed that search for the parameters of a source, including its sky position. Having now put these codes in place we are investigating their viability for use with triggered searches.

Search of gamma-ray pulsars through the adaptation of methods used for the search of continuous gw signals

Tringali M , Astone P, Colla A, Frasca S, Palomba C

The search of continuous gravitational wave signals from spinning neutron stars and of gamma-ray pulsar share several aspects. In both cases a semi-periodic signal, affected by various kinds of modulations, is searched into the data and long integration times are necessary to improve the signal to noise ratio to the detectability level. This implies the need for a very accurate correction of the Doppler effect, pulsar spin-down and also smaller relativistic effects such as the Einstein delay. In this work we present a method for the blind search of gamma-ray pulsars which is based on techniques developed for the search of continuous gravitational wave signals from spinning neutron stars. Result of tests consisting in the semi-blind analysis of Fermi data in a small region of the parameter space around a few already identified pulsars are described.

Probing compact star interiors with gravitational waves, radio waves and x-rays

Schwenzer K

Oscillation modes present a direct way to probe the properties of the interior of a neutron star. Unstable r-modes, in particular, can be a significant source of gravitational waves in rapidly spinning stars. We study the continuous gravitational wave emission of such sources via a semi-analytic approach that allows to estimate the various uncertainties in the system. We find that the frequency to which r- modes spin down a young neutron star as well as the characteristic gravitational wave strain amplitude are extremely insensitive both to microscopic and macroscopic details. This is important for future continuous gravitational wave searches and we discuss promising candidates. Further, we present a novel connection of the r-mode evolution to precise timing data of radio pulsars and discuss the compatibility of different forms of dense matter.

203 Factors limiting sky localization of gravitational-wave sources

Drago M , Klimenko S, Mazzolo G, Necula V, Prodi G, Re V, Salemi F, Tiwari V, Vedovato G, Yakusin I

Electromagnetic counterparts are expected for some types of gravitational-wave (GW) signals. Observa- tion of such counterparts strongly depend on the sky localization capabilities of the GW detector net- works. We show how the source localization performance of the analysis methods developed to search for un-modeled transient signals compares with the theoretical expectations from the triangulation method based on measurements of the arrival time of the GW signal at different detectors. We discuss the fac- tors which limit the GW source localization, and we show how to improve the performance beyond the expectations for the triangulation method. Our investigation is based on simulated data of Advanced Detector networks, and makes use of software signal injections for different polarization states.

Prompt searches for optical signal from gravitational wave transients with pi of the sky

Zadrozny A

Pi of the Sky is a robotic telescope project dedicated to observations of short time astrophysical phenom- ena, especially for optical counterparts of GRBs. Two observation sites are located on both hemispheres, one in Chile and one in Spain, covering the field of view of 400deg2 and 1600deg2, respectively. Images are taken with time resolution of 10s. Such a wide field of view system can also be very useful in searched for other optical transients. An observation of an astrophysical event in both gravitational and optical band might bring very sig- nificant scientific results and could be the first step toward the direct detection of gravitational waves. The main aim of the LoocUp project, initiated by LSC and Virgo collaborations and several other elec- tromagnetic (EM) observation teams, was to try to find such a coincidence by doing an electromagnetic follow-up of the most promising GW event candidates selected by the low-latency analysis of LIGO and Virgo detector data. During the future joint GW-EM observations, a new Pi of the Sky telescope unit, could image more than 1/3 of GW candidate probability maps in less than 10 minutes. The system could automatically recognize optical transients and perform follow-ups of interesting events. The aim of the talk is to show methods used by Pi of the Sky team to search for optical counterparts of GW event candidates as part of the future LookUp and usefulness of large field of view telescopes in such searches.

Magnetar burst oscillations and multi-messenger astronomy

Jones D

Magnetars are extremely interesting targets for multi-mesenger astronomy. Their powerful X-ray bursts will be accompanied by some level of gravitational wave emission. Indeed, X-ray-triggered gravitational wave searches have already been carried out. However, the way in which such searches should be performed depends upon the frequencies and decay times of the modes excited. In this talk I will describe some recent estimates of the decay times of the oscillations, relate these to the physical processes at work, and discuss the significance for multi-messenger astronomy.

204 C9 - Experimental gravitation

Oral session

Interferometry with bose-einstein condensates in microgravity

Ahlers H , Rasel E, Ertmer W

Atom-chips employed as a source for ultra cold atoms promise a new window of precision for atom inter- ferometers. They allow for a strong reduction in complexity of the atomic preparation and an increase in robustness of the sensor. Moreover, innovative designs of the chips allow to achieve a high flux of ultra-cold atoms. We report on a Bragg-type asymmetric Mach-Zehnder interferometer operated with a chip-based atom laser in microgravity which allowed us to study the coherence over hundreds of millisec- onds. With the chip providing delta-kick cooling and an RF-transfer to a nonmagnetic state, we reduced the expansion rate of our 87Rb Bose-Einstein condensate (BEC) and extended its observation time up to 2s. This kind of control is crucial for proposed high precision interferometers, e.g. STE-QUEST, where sub-nanokelvin expansion rates of two atomic species will have to be matched precisely to limit systematic errors for a test of the equivalence principle. To work towards making atom interferometry accessible for space applications, we developed a novel source concept for the ZARM drop-tower and a sounding rocket mission within the QUANTUS Project. Based on a three layer atom-chip and loaded from a cold atomic beam, it combines efficient capturing and trapping with rapid evaporative cooling and generates about 4 × 105 ultra-cold atoms in less than 2s.

Ste-quest: testing einstein equivalence principle in space

Jetzer P

Space-Time Explorer and QUantum Equivalence Principle Space Test (STE-QUEST) is a space mission conceived to test different aspects of the Einstein Equivalence Principle by using a high stability atomic clock, which will measure the gravitational time dilation effect, and an atom interferometer which will compare the free fall of two rubidium isotopes. The instrument sensitivity is specified to test the uni- versality of the free propagation of matter waves to an uncertainty in the Eotvos parameter better than 1 × 10−15. STE-QUEST is a M class mission proposed within the Cosmic Vision programme of ESA and selected for an assessment study as a candidate for the M3 mission with a flight opportunity in 2022-2024. I will give a review of the current status of the project and of its scientific capabilities for testing different aspects of General Relativity Theory.

205 Quantum test of the equivalence principle: the ste-quest mission

G¨urlebeck N , Gaaloul N, Herrmann S, Schubert C, Schuldt T, Hartung J, Braxmaier C, Rasel E, and the STE-QUEST consortium

STE-QUEST (Space-Time Explorer and Quantum Equivalence Principle Space Test) aims for a test of General Relativity by testing the Universality of Free Fall with a dual species atom interferometer on a satellite. This test is based on measuring the differential acceleration of two test bodies assumed to be zero by Einstein’s Equivalence Principle (EP). The E¨otv¨osratio derived from the differential signal will be determined with an accuracy of parts in 10E15 beyond the state-of-the-art precision of 10−13 established by lunar laser ranging and torsion balances. Bose-Einstein condensates of Rb87 and Rb85 will act as test bodies in the dual species interferometer so that this will constitute a quantum test of the EP. The matter waves will be simultaneously prepared and interrogated with a free evolution time of 10 s, which is possible due to the conditions in space. − m Within a single cycle of 20s, a sensitivity of accelerations of 3 12 s2 is anticipated, which is limited by shot noise. The simultaneous interferometry is carried out in double diffraction Mach-Zehnder geometry, which allows a high suppression of noise and bias terms. In the talk, the measurement principle will be presented, an overview of the preliminary payload design will be given, and the estimated error budget will be discussed. STE-QUEST is a proposal for an M3 mission in the frame of the Cosmic Vision program of ESA.

Matter wave - laser based interferometer gravitation antenna (miga)

Bouyer P

I will present the Matter wave - laser based Interferometer Gravitation Antenna (MIGA) project, which concerns the construction of a novel infrastructure to study strain tensor of space-time and gravitation. Using a novel approach for strain measurement, based on quantum mechanics, this infrastructure will allow for deeper understanding of the earth’s gravity field over a very broad band, from frequencies of less than 1 cycle per second to those in excess of hundreds of hertz. The applications of MIGA extend from monitoring the evolution of the gravitational field to providing a new tool for detecting gravitational waves. By combining geophysics and fundamental physics application in a single infrastructure, MIGA will lead to an unprecedented step in understanding geophysical phenomena and will allow for enhancing existing and future gravitational wave detectors.

Laser ranging for grace follow-on

Sch¨utzeD, M¨ullerV, Stede G, G¨orthA, Gerberding O, Mahrdt C, Sheard B, Heinzel G, Danzmann K

The satellites of the Gravity Recovery and Climate Experiment (GRACE) mission use satellite-to-satellite tracking via microwave ranging to collect data about spatial and temporal variations in the gravity field of the Earth. A GRACE Follow-On mission will be launched in 2017. The GRACE Follow-On satellites will contain a Laser Ranging Interferometer in addition to the microwave ranging system to improve the inter- satellite distance measurements. This Laser Ranging Interferometer uses heterodyne interferometry with active transponder principle and phasemeter readout making use of LISA technologies. Essential parts of the Laser Ranging Interferometer include a Triple Mirror Assembly to establish an off-axis roundtrip path between the satellites and a steering mirror setup to account for satellite pointing. A laboratory test setup of the GRACE Follow-On interferometer is presented with which these key components are tested.

206 Testing lorentz invariance and fundamental constants with precision clocks and oscillators

Tobar M

We present long-term analysis of the frequencies of 3 separate Cs fountain clocks and one Rb fountain clock with respect to various hydrogen masers in the LNE-SYRTE atomic clock ensemble. We search for periodic changes correlated with the solar gravitational potential at the Earth and boost with respect to the Cosmic Microwave Background (CMB) rest frame. The data sets span more than eight years. The main sources of long-term noise in such experiments are the offsets and linear drifts associated with the various H-masers. The drift can vary from nearly immeasurable to as high as 1.3 × 10−15 per day. To circumvent these effects we apply a numerical derivative to the data, which significantly reduces the standard error when searching for periodic signals. We determine a standard error for the putative Local Position Invariance (LPI) coefficient with respect to gravity for a Cs-Fountain H-maser comparison of −6 −5 |β − βCs|leq4.8 × 10 and |βH − βRb|leq10 for a Rb-Fountain H-maser comparison. From the same data the putative boost LPI coefficients were measured to a precision of up to parts in 1011 with respect to the CMB rest frame. By combining these boost invariance experiments to a Cryogenic Sapphire Oscillator versus H-maser comparison1, independent limits on all nine coefficients of the boost violation vector with respect to fundamental constant invariance (fine structure constant, electron mass and quark mass respectively), were determined to a precision of parts up to 1010.

Solar system tests of mond and modified gravity theories

Ni W

The observed regularities in the properties of dwarf galaxies and the correlation between observed mass discrepancies and acceleration may indicate that there needs a change a paradigm in cosmology and theory of gravity. This situation has driven the building of modified dynamics and modified gravity as alternatives to dark matter theories. MOND (MOdified Newtonian Dynamics) theories deviate from Newtonian dynamics and general relativity significantly at gravity accelerations around the 10- 10 ms- 2 level. This can be tested directly by spacecraft like LISA Pathfinder to pass through the Sun–Earth Saddle point where the gravity accelerations are small and has been considered and analyzed. It can also be tested by laser ranging to measure effects on light propagation and to measure the cumulative effects on spacecraft trajectory. In this paper we will look into present and potential future tests/constraints on these theories from solar-system experiments/observations as a guide of theory-building. Positions of saddle points of the total gravitational potentials are important to these tests. We estimate the saddle points in various theories taking into consideration of the effects from cosmology, Galaxy to our solar system as total potential depends on all these.

Tests of gravity theories with binary pulsars

Freire P

In this presentation, I will summarize some of the recent tests of gravity theories using binary pulsars. First, I talk about the double pulsar and discuss its use as a precision test of general relativity. Following this, I discuss several recent experiments which use, for the first time, millisecond pulsar - white dwarf systems. The asymmetric nature of these systems allows stringent constraints on dipolar gravitational wave emission; these result on very tight constraints on several classes of alternative theories of gravity, particularly when combined with the measurements from the double pulsar. Furthermore, these tests can now be made using massive pulsars which allow for the first time a study of the properties of gravity

207 in an extreme regime that has never been probed before. I then present some recent constraints on Local Lorenz Invariance (LLI) of gravity derived from recent pulsar measurements, which represent gains of many orders of magnitude over previous limits on LLI violation. Finally, I discuss a new test of the Strong Equivalence Principle, which might provide greatly improved limits on any possible violation of this general physical principle.

Reconstruction of gravitational potential at the galactic center with observations

Zakharov A

There are two observational ways to reconstruct gravitational potential at the Galactic Center, namely, observations of the smallest spot (shadow) and evaluation of its size (and shape in the future). From these observations one could evaluate parameters of black hole such as its mass, spin and charge. Surprisingly, current measurements of shadow sizes are better fitted with Reissner–Nordstrom black hole in comparison with Schwarzschild one. We also discuss an opportunity to evaluate black hole parameters from analysis of bright star orbits. One could evaluate parameters of bulk distribution of matter for this case. From these observations one could find constraints on alternative theories of gravity such as f(R) for instance, Rn and Yukawa gravity in particular. From our analysis of S2 star orbit we found that parameters of Rn theory have to be very closed values corresponding to GR ones, while for Yukawa gravity the best fit give δ parameter which is very close to value obtained recently for spiral galaxies.

Lunar laser ranging tests of general relativity

Mueller J , Biskupek L, Mai E, Hofmann F

In 1969, a new era for studying relativity has started. With the first returns of laser pulses sent from observatories on Earth to reflector arrays on the Moon, a new space technique – Lunar Laser Ranging (LLR) – has been providing an ongoing time series of highly accurate Earth-Moon distance measurements. To enable data analysis at the mm level of accuracy, all elements of the tracking process have to be modeled at appropriate (relativistic) approximation, i.e. the orbits of the major bodies of the solar system, the rotation of Earth and Moon, the signal propagation, but also the involved reference and time systems. We will show where relativity enters the LLR analysis and how the whole measurement process is modeled, including the major classical (Newtonian) effects like gravity field of Earth and Moon, tidal effects, ocean loading, lunar tidal acceleration (that causes the increase of the Earth-Moon distance by about 3.8 cm/year), etc. By analysing the 43-year record of range data, LLR is one of the best tools to test General Relativity in the solar system. It allows for constraining gravitational physics parameters related to the strong equivalence principle, Yukawa-like perturbations, preferred-frame effects, or the time variability of the gravitational constant. We will present recent results for the various relativistic parameters.

Testing finsler geometry in the solar system

Laemmerzahl C , Perlick V, Hasse W

The usual framework to describe tests of Einstein’s General Relativity is given by the parametrized post-Newtonian framework (PPN) which is based on a Riemannian geometry. Here we present a new framework which is also capable to include effects due to a (hypothetical) Finslerian geometry.

208 After some introductory discussion of the definition of Finsler spacetimes and their symmetries, we consider a class of spherically symmetric and static Finsler spacetimes which are small perturbations of the Schwarzschild spacetime. The deviations from the Schwarzschild spacetime are encoded in three perturbation functions which have the following interpretations: the first perturbs the time function, the second the radial length measurement and, finally, the third introduces a spatial anisotropy which is a genuine Finsler feature not present in the PPN framework. We work out the equations of motion for freely falling particles and for light rays, i.e., the timelike and lightlike geodesics, in this class of spacetimes, and we discuss the bounds placed on the perturbation functions by observations in the Solar system, that is, (i) free fall, (ii) the perihelion shift, (iii) light deflection and (iv) gravitational time delay. We close with an outlook (i) for further generalizations of the framework and (ii) for further tests.

On the potential of atomic clocks

Bondarescu R, Bondarescu M, Jetzer P, Hetenyi G, Boschi L, Balakrishna J

Since the atomic second became a standard of time, atomic clocks have increased in accuracy by an order of magnitude a decade. They have been aboard GPS satellites for many years. The Atomic Clock Ensemble in Space (ACES) and the Space-Time Explorer and QUantum Equivalence Principle Space Test (STE-QUEST) plan to put even more accurate atomic clocks in space. These clocks will be accurate, stable and portable. I will discuss simple estimates that suggest that atomic clocks could be useful in many areas. The use of clocks in geophysics would be a first direct application of general relativity, which predicts that clocks tick slower near heavy objects, to our every day life. We find that atomic clocks that can measure a frequency change of ∆f/f 10−18 would be sensitive to geoid perturbations caused by a buried sphere of radius of 1 km with 20% density anomaly. Such clocks could be used to provide local geoid maps (the equipotential surface of the Earth that approximates the mean sea level and accounts for all sub-surface density variations) or improve our understanding of volcanoes. They have different depth sensitivity than gravimeters and joint surveying could result in a better understanding of underground structure.

Optical ion clocks - aplications from relativistic geodesy to fundamental tests

Mehlstaeubler T , Schmidt P, W¨ubbena J, Keller J, Leroux I, Amairi S, Scharnhorst N, Burgermeister T, Partner H

Time and frequency are the most accurately measurable quantities today. In particular, optical clocks, that nowadays can reach a relative frequency inaccuracy as low as 10−17, will open up a new field of search for deviations in the predictions of Einstein’s general relativity, tests of modern unifying theories and the development of new sensors for gravity and navigation. In my talk, I will introduce the concepts of optical ion clocks, present the status of clock development at PTB and discuss projects and future applications in relativistic geodesy and for fundamental tests of physics models.

209 Applying optical lattice clocks for relativistic geodesy: status and upcoming experiments

Falke S, Vogt S, H¨afnerS, Sterr U, Lisdat C

Relativistic geodesy applies the gravitational redshift of clocks to determine the gravitational potential and thus the height above the geoid. Due to high accuracy and stability of optical clocks this method can now be applied in geosciences. While gravimeters measure the gradient of the geopotential, the frequency comparison of clocks probes the potential difference itself. The accuracy of current laboratory optical clocks corresponds to a height difference of a few cm and their stability allows measuring this within an hour, which becomes important if interested in the time dependence. Noise cancelled optical fibre links cover distances between the clocks of several hundred km without limiting the performance. Optical lattice clocks have demonstrated the best stabilities among optical clocks due to parallel interrogation of several thousands of reference atoms. The performance of our stationary strontium lattice clock will be matched by a transportable clock we currently assembled. Our clocks are used in a collaborative project of European metrology institutes within the EMRP programme: A proof-of-principle experiment of relativistic geodesy will compare two clocks separated by 100 km of distance and 1000 m of elevation. This program aims on improving timescales by incorporating geophysical models. We are also involved in the space optical clock project that builds transportable optical lattice clock demonstrators following the roadmap for improved clocks to space.

Data simulation and analysis for the aces mission

Le Poncin-Lafitte C , Delva P, Meynadier F, Guerlin C, Wolf P, Laurent P

The Atomic Clocks Ensemble in Space (ACES), which will be installed on board ISS in 2016, will realize in space a time scale of very high stability and accuracy. This time scale will be compared to a ground clock network thanks to a dedicated two-way microwave link. The altitude difference between the ACES clock and ground clocks will allow to measure the gravitational redshift with unprecedent accuracy as well as looking for a violation of Lorentz local invariance. Several ground clocks based on different atomic transitions will be compared to look for a drift of the fine structure constant. Moreover, the mission will pave the way to a new type of geodetic measurement: the gravitational redshift will be used to measure gravitational potential differences between distant clocks, with an accuracy around 10cm. Our team is involved in the design and development of the data processing software : from theoretical modeling and numerical simulations at the required precision to the development of a data analysis software. Our team is working on a wide range of problems that need to be solved in order to achieve the required stability in almost real time.We present some key aspects of the measurement, as well as current status of the software’s development, including the results of tests with simulated data. We put particular emphasis on the scientific products that will be provided to the users and discuss how those products can be used for the purposes of time/frequency metrology.

Matter-waves studies of the effects of gravity on quantum systems

Mueller H

The phase of a matter wave is proportional to the proper time experienced by the particle. This key principle of relativistic quantum mechanics has allowed us to perform tests of general relativity that yield the most sensitive current bounds on parameters describing equivalence principle violations in the Standard Model Extension. The bounds can be further sharpened by taking into account the composition

210 of nuclear matter and the kinetic energy of protons and neutrons in nuclei. We have also built a rest- mass clock which uses the mass of a single particle as a reference, combining a Ramsey-Borde atom interferometer with a femtosecond optical frequency comb. The clock has an accuracy and stability of 4 × 10−9. We will discuss future experiments testing the equivalence principle with dual-species interferometry, the gravitostatic Aharonov-Bohm experiment, and testing the equivalence principle for free electrons and even positrons by measuring the gravitational redshift of a proposed electron rest-mass clock.

Drag-free requirements for a shapiro time-delay mission based on an optical clock near the earth-sun l-1 point

Bender P, Ashby N, Dolesi R, Weber W

The future space-qualification of optical clocks will make possible a much more accurate determination of the Shapiro time-delay using measurements between spacecraft. One approach would involve laser time-delay measurements from a spacecraft that contains an optical clock, in orbit around the L-1 point, to a transponder spacecraft in a two year period orbit around the Sun (Ashby and Bender, 2011; Ashby et al., 2009). The measurements would be made around superior conjunction, when the line of sight to the distant spacecraft passes by the Sun. However, in addition to the stability requirement on the clock, both spacecraft must have very good drag-free performance over periods of at least 8 days, and hopefully 20 days, around conjunction. Since the transponder spacecraft will be near aphelion at this time, the spacecraft temperature should vary by less than 0.1 K during the 20 day period, even without active control. However, the requirements on the L-1 spacecraft orbit in order to avoid thruster firings over this period, to permit highly accurate orbit determination, and to keep the temperature stable need to be investigated. The level of the uncorrected relative spacecraft displacements over this period due to spurious accelerations needs to be less than roughly 10 microns.

General relativity measurements and constraints in gravitation theories with laser ranging to the two lageos satellites

Lucchesi D, Peron R

Einstein theory of General Relativity (GR) represents a metric theory for the description of the gravita- tional interaction whose predictions, especially in the Weak-Field and Slow Motion limit, have success- fully passed a deep experimental investigation during last decades. Besides GR, other metric theories of gravitation have been proposed. A way to discriminate, from the experimental point of view, among the different theories is through the PPN formalism. Among the PPN parameters, the most important are beta and gamma. We present the results of an analysis of the orbit of the two LAGEOS satellites that allowed us to measure the cited parameters in the field of the Earth. We determined the orbit of the two satellites and then analyzed and fitted the orbital residuals in the node longitude and argument of pericenter. The former is sensitive to the Lense-Thirring and de Sitter precessions, while the latter is mainly sensitive to the Schwarzschild precession. In particular, from the argument of pericenter of LA- GEOS II we estimated a linear combination of the two parameters, while from a suitable combination of the two nodes we obtained gamma. From the measurement of the pericenter shift we derived significant constraints in alternative theories of gravitation. This work also represents the first measurement of the de Sitter precession with Earth-orbiting artificial satellites. Finally, the impact of the main systematic error sources on the above measurements is discussed.

211 GReAT: a cryogenic differential accelerometer to test eep to a few parts in 1015

Iafolla V, Fiorenza E, Lefevre C, Lucchesi D, Lucente M, Magnafico C, Nozzoli S, Peron R, Santoli F, Lorenzini E, Shapiro I

At the foundation of general relativity (GR) is Einstein Equivalence Principle (EEP) which relies on the Weak Equivalence Principle (WEP). WEP is based on the principle that the ratio of the gravitational mass to the inertial one is the same for all bodies, hence all fall with the same acceleration independently of their mass and composition. This is the Universality of Free Fall (UFF) a WEP consequence. Tests for UFF are the most significant to verify GR and the most promising to discover new physics beyond it. An accuracy of 10−13 has been presently reached. GReAT is a proposed experiment aimed at testing UFF/WEP with an accuracy of about 10−15 by a differential accelerometer free falling inside a co- moving cryogenic evacuated capsule released from a stratospheric balloon. The detector is spun about an horizontal axis to modulate a possible violating signal at the spin frequency in order to distinguish the violation from other effects. The high accuracy requires resolving a very small signal out of components like the instrument intrinsic noise and the noise components associated with its motion and gravity gradients. We describe a cryogenic prototype that consists of two self-differential accelerometers (one assembled with different materials) capable of rejecting linear and angular noise while retaining the possible violation signal. We discuss the development and testing of the instrument and preliminary results at a temperature of 11 K with a quality factor of 130000.

Two-body spin and orbital precession: theory and experimental verification and the role of hidden momentum

O’Connell R

We proceed from the microscopic to the macroscopic by adopting the universality of the gravitational interaction. We use a Lagrangian-Hamiltonian approach for the calculation, from which the spin preces- sion readily follows. The orbital precession is simplified by making use of the Runge-Lenz vector and, in particular, the fact that it always remains perpindicular to the orbital angular momentum while both are precessing. In addition, we explain how hidden momentum plays a role and its close connection with spin supplementary conditions and the non-trivial relation between momentum and spin.

Ginger and ginger pf (gyroscopes in general relativity)

Di Virgilio A

The purpose of the GINGER is to perform the first test of general relativity (not considering the gravi- tational redshift measurements) in a terrestrial laboratory, using light as a probe. The experiment will complement the ones in space, performed or under way, with an entirely different technique and at a far lower cost. The methodology is based on ring-lasers, which are extremely accurate rotation sensors and can not only sense purely kinematical rotations (Sagnac effect accounting for the Earth rotation, polar motion of the terrestrial axis, local rotational movements of the laboratory due to the Earth crust dynamics...), but also general relativistic contributions such as the de Sitter effect (coupling between the gravito-electric field of the earth and the kinematical rotation) and the Lense-Thirring effect (inertial frame dragging due to the angular momentum of the earth). In order to reveal the latter effects, ring-laser response must be improved to be able to measure the effective rotation vector (kinematic plus GR terms) with an accuracy of 1 part in 109 or better. This is a challenging technological aspect, which however has been accurately taken into account by designing as system of ring lasers that will be implemented in this project. GINGER and its path-finder will be described.

212 Optical/thermal analysis of dust degradation for the lunar laser ranging retroreflector for the 21st century

Currie D, Murphy T, Delle Monache G, Dell’Agnello S

The retroreflectors deployed on the Apollo 11, 14 and 15 missions are still operating after forty years and providing new and unique science. In particular, the results of the Lunar Laser Ranging Program (LLRP) have produced some of the best tests of Gravitation and Relativity theories. The LLRP tests the various proposed theories that encompass the recent observations that seem to either violate GR or require new physics, i. e., Dark Matter and Dark Energy. The ranging accuracies of the laser observatories have improved by a factor of 200 so the uncertainty in the single photo-electron ranges is the limiting accuracy. We are now engaged in the design of the next generation retroreflectors, the Lunar Laser Ranging Retroreflector for the 21st Century (LLRRA-21). During the lunar night, the photon return rate is only 10% of the expectation, while at lunar noon, it is only 1%. Understanding this effect is critical in the design of LLRRA-21. The primary candidates are dust on the CCR and/or UV darkening. Recent observations during a lunar eclipse have provided some critical information, since the variation of the solar intensity is matched to the thermal time constants of the retroreflectors. To address this, we have developed detailed optical/thermal simulations, performed experiments in the CCLAS dust accelerator in addition to the eclipse observations. These results will be described and then compared with models of the expected dust environment on the lunar surface.

Status and perspectives of the lisa pathfinder gravitational reference sensor on ground testing with torsion pendulum

Russano G, Cavalleri A, De Rosa R, Di Fiore L, Dolesi R, Garufi F, Grado A, Tu H, Hueller M, Vitale S, Weber W, Wen S

Torsion pendulums has been successfully developed to measure small forces at level that allows for on ground significant investigation of disturbances acting on nominally free falling test masses for spaceborne gravitational waves observatories operating in the mHz frequency region. An extensive experimental campaign is ongoing to consolidate the noise model for stray forces originated in the Gravitational Reference Sensor that surrounds the test mass, and we present here the status and the perspectives of our investigations on a GRS Replica of the flight model developed for the LISA Pathfinder mission.

213 Poster session

Testing chameleon scalar fields with ste-quest

Scharer A, Bondarescu R, Jetzer P, Lundgren A

STE-QUEST provides a unique possibility to constrain chameleon scalar field models where the coupling to matter depends on the surrounding matter density. In dense environments such as on the surface of the Earth the effective mass of the scalar particle becomes very large, suppressing the fifth force mediated by the field. In space, the small background density allows a positive detection of such a fifth force at a level that already has been excluded by experiments on Earth. If the scalar field couples differently to different species of matter, this causes a violation of the universality of free fall. In this poster, we show how STE-QUEST can constrain chameleon models which couple differently to the two Rb isotopes used in the atom interferometer on-board the satellite. Additionally, the presence of such a scalar field causes the gravitational red shift to deviate from the one expected in general relativity. Therefore the accurate tracking of the satellite on its elliptical orbit together with the atomic clock can further constrain chameleon models.

Kinetic energy and violations of einstein’s equivalence principle

Hohensee M, Mueller H

According to Einstein’s equivalence principle (EEP), the laws of physics are the same in any freely falling frame, and the acceleration of free fall is the same for all objects, be they electrons, protons or neutrons, matter or antimatter. Though the EEP has been verified with high precision for normal matter, its validity for antimatter is less certain. We explore the role of a particle’s bound kinetic energy in quantum and classical tests of the EEP in the context of the Standard Model Extension (SME). We show how EEP violation for free electrons manifests as anomalous gravitational redshifts in the energy of electronic transitions, in proportion to the bound electrons’ kinetic energy. This framework also describes theories in which EEP is satisfied for matter, but violated by antimatter. We show that tests of EEP on bound systems of normal matter can nevertheless indirectly constrain EEP-violation in antimatter, thanks to corrections from the systems’ bound kinetic energy. Using a Woods-Saxon potential to calculate the bound kinetic energy of a wide range of atomic nuclei, we infer the sensitivity of existing and planned experiments to EEP violation specific to antimatter, and improve existing limits on EEP violation by up to a factor of ten.

Measuring the speed of gravity in a laboratory with a dnf generator, micro-resonators and 1.2ghz laser vibrometers

Cagnani I

The theoretical assumption that the speed of propagation of gravitational fields is equal to the speed of light in vacuum has never been tested in a laboratory setting. This experiment represents the first attempt of a direct measurement of this fundamental parameter. A Dynamical Newtonian Field is created by rotating in the horizontal plane two identical stacks of steel discs at the same distance from their axis. Two micro-oscillators, with reflective cubic test masses and placed one 2.5 m closer to the DNF source than the other, are driven gravitationally to mechanical resonance. Any non-infinite propagation speed

214 of the field must cause a phase difference between the two oscillators. If the speed of gravity equals the speed of light, a 8.3 ns phase difference is expected. Measuring this phase difference requires an ultra high frequency laser Doppler vibrometer for each oscillator. Polytec(R) 1.2GHz microscope laser vibrometers are used, allowing a 0.8 ns temporal resolution. A precise 1.2GHz signal is sampled along the output of the two vibrometers. In data analysis, the phase difference is obtained from the average number of 1.2GHz waves occurring between the matching zeros (inversion points) of the two oscillators. For isolating the micro-oscillators from ground vibrations, negative-stiffness passive vibration isolators from Minus-k(R) are used while vacuum optical chambers provides environmental isolation.

215 Joint session D1, D2 and D4: The Quantum Mechanics of Black Hole Evaporation

Oral session

Information loss

Wald R

We review the arguments in favor of loss of information in the process of black hole formation and evaporation.

Why is the generalized second law true?

Wall A

The entropy outside of an event horizon can never decrease if one includes a term proportional to the horizon area. For a long time, this astonishing result had only been shown for quantum fields that are in an approximately steady state. I will describe a new proof of the generalized second law for arbitrary slices of semiclassical, rapidly-changing horizons. I will start with the simplest case, Rindler horizons, and then describe how the proof can be adapted to other cases (black holes, de Sitter, etc.) by restricting the field algebra to the horizon. The generalized second law holds because the horizon is invariant under a larger symmetry group than the rest of the spacetime.

Quantum space-times and unitarity of bh evaporation

Ashtekar A

There is growing evidence that, because of the singularity resolution, quantum space-times can be vastly larger than what classical general relativity would lead us to believe. We review arguments that, thanks to this enlargement, unitarity is restored in the evaporation of black holes. In contrast to ADS/CFT, these arguments deal with the evaporation process directly in the physical space-time.

216 Dynamical evaporation of quantum horizons

Pranzetti D

We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation applied to this fundamental discrete structure. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. We investigate the final stage of the evaporation process and show how the dynamics leads to the formation of a massive remnant. Implications for the information paradox are discussed.

Black hole information from the viewpoint of string theory

Horowitz G

We review the contributions that string theory has made to understanding black hole information. This includes the remarkable gauge/gravity duality and the counting of microstates of certain black holes. We also comment on more speculative ideas including fuzzballs and final state boundary conditions.

Ads/cft, unitary black hole evaporation, and firewalls

Marolf D

We review arguments that black hole evaporation is unitary in AdS/CFT. As a result, the physics expe- rienced by infalling observers at the horizon of at least sufficiently old black holes described by AdS/CFT must be dramatically different from that described by familiar field theory in a smooth spacetime.

Falling into a black hole and the information paradox in ads/cft

Papadodimas K

I will describe how the interior of a black hole can be reconstructed from the point of view of the dual gauge theory in the framework of the AdS/CFT correspondence. I will argue that the infalling observer does not notice anything special when crossing the horizon and that it is possible to resolve the information paradox without dramatic violations of effective field theory, in contrast to predictions by the recent fuzzball and firewall proposals.

217 D1 - Loop quantum gravity and spin foams

Oral session

Complete quantization of vacuum spherically symmetric gravity

Pullin J

We find a rescaling of the Hamiltonian constraint for vacuum spherically symmetric gravity that makes the constraint algebra a true Lie algebra. We can implement the Dirac quantization procedure finding in closed form the space of physical states. New observables without classical counterpart arise. The metric can be understood as an evolving constant of the motion defined as a quantum operator on the space of physical states. For it to be self adjoint its range needs to be restricted, which in turn implies that the singularity is eliminated. One is left with a region of high curvature that tunnels into another portion of space-time. The results may have implications for the current discussion of ”firewalls” in black hole evaporation.

On the quasilocal first law for isolated horizon and its uses in the euclidean partition function

Frodden E, P´erezA

In this talk I will discuss a new quasilocal black hole energy proposal, it is based on near horizon observers and is suitable for loop quantum gravity statistical computations. I will also present a simple application of this energy notion in the context of Euclidean partition function.

Black hole entropy and entanglement in spinfoam gravity

Bianchi E

I report recent progress on the study of entanglement entropy in spinfoam quantum gravity, and its rela- tion with the Bekenstein-Hawking area law. Based on arXiv:1212.5183 in collaboration with R.Myers.

218 An analysis of the cghs model in new variables

Rastgoo S

We present a Hamiltonian analysis of a general class of 2D gravitational systems coupled to matter. In this class we focus on a specific case, the CGHS model, which is a dilatonic system coupled to matter. The previous Hamiltonian analyses of this model have been mostly within the metric formulation and based on a conformal transformation. We perform an analysis based on tetrad variables without conformal transformation, derive new (Ashtekar-like) variables for the model and solve the system completely classically. Then we find a local true Hamiltonian for the massive case.

Microcanonical entropy of isolated horizon and fixation of the barbero-immirzi parameter

Majhi A

In quantum geometry, the effective description of a Quantum Isolated Horizon(QIH) is given by a 2+1 dimensional Chern-Simons(CS) theory on the Isolated Horizon(IH) coupled to the punctures made by the bulk spin network on the smooth IH. The level of the CS theory(k) and the total number of punctures(N) on the QIH characterize the macrostates of the QIH. The microcanonical entropy of QIH can be expressed completely in terms of k and N. For the microcanonical entropy to obey the Bekenstein-Hawking area law, the Barbero-Immirzi(BI) parameter has to be fixed within a range of real values 0.159 and 0.225. The derivation of the microcanonical entropy directly from the CS theory, using usual equilibrium statistical mechanics, shows the self-completeness of the QIH framework. Moreover, the BI parameter, which is present both in the bulk and the boundary(QIH) theory, gets determined by the boundary theory only. It may be a hint towards a bulk-boundary correspondence in loop quantum gravity much like the AdS-CFT correspondence in string theory.

The entropy of btz black hole from loop quantum gravity

Wang J , Ma Y

In this work, we study the entropy pf the BTZ black hole in the framework of the loop quantum gravity. We find that the horizon degree of freedom can be described by a topological field theory–BF theory. We count the number of the horizon states that compatible with the macroscopic horizon length to give the entropy and find that the entropy obey the area law.

Anomaly free constraint algebra for a weak coupling limit of gravity

Varadarajan M

The G–¿0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. The Poisson bracket algebra of its Hamiltonian and diffeomorphism constraints is isomor- phic to that of gravity, the constraint algebra containing structure functions as in gravity. We construct a nontrivial anomaly free representation of the constraint algebra of this model based on Loop Qunatum Gravity type representations. The strategy is to first tackle the commutator between a pair of Hamilto- nian constraints ignoring issues of spatial covariance and, subsequently, to incorporate spatial covariance.

219 We provide an overview of this work, the first part of which was carried out in collaboration with Casey Tomlin. This work is a precursor to a similar construction, in progress, for full blown (Euclidean) LQG.

Shape dynamics and quantum gravity

Koslowski T

The Shape Dynamics formulation of General Relativity shows that the construction principle of quantum gravity does not have to be based on spacetime geometry, but can instead be based upon the dynamics of spatial conformal geometry. This opens a number of new perspectives for quantization programs of gravity. I will present some progress in the application of the loop quantization- as well as in the polymer quantization framework to Shape Dynamics and discuss what the open problems are.

Time and a physical hamiltonian for quantum gravity

Husain V

We describe a complete quantization of general relativity coupled to pressureless dust in the framework of loop quantum gravity. The dust field provides a preferred time variable, and gives a corresponding physical Hamiltonian that is functionally of the same form as the time reparametrization constraint. This Hamiltonian, together with spatial diffeomorphism constraint, characterize the classical theory in the dust time gauge. The quantum theory is constructed by realizing the hamiltonian as an operator on the space of diffeomorphism invariant spin networks. The approach opens up a path to concrete calculations in model systems such as gravitational collapse and black hole formation in spherical symmetry, and raises the question of what is the corresponding spin foam model.

A quantum ricci operator for lqg

Assanioussi M

We introduce a new operator in Loop Quantum Gravity - the 3d curvature operator - corresponding to the classical 3-dimensional Ricci scalar. The construction is based on the concepts of Regge Calculus. We define this operator starting from the classical expression of Regge curvature, then we derive some of its properties and discuss some explicit checks of its semi-classical behavior.

Construction of dirac observables for general relativity with the use of geometry

Swie˙zewskiJ´

In my talk I will present a proposal for the construction of Dirac observables for General Relativity. The construction relies on the use of geometrically defined coordinates with a clear physical interpretation. I will discuss some problems of the construction and turn to a similar construction of observables for a simplified theory of General Relativity coupled to a dust field.

220 Scalar material reference systems and loop quantum gravity

Giesel K

Scalar fields as material reference systems have been used in the context of loop quantum gravity in order to solve (part) of the constraints of general relativity already at the classical level before the quantization is performed. Depending on the particular choice of the reference fields one obtains different reduced phase spaces and after quantization different models for the quantum theory. We will discuss the similarities and differences of those models particularly with regard to their dynamics in the quantum theory.

Quantum isotropy and dynamical quantum symmetry reduction

Engle J

We give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which can be quantized, yielding a definition of a diffeomorphism-invariant, homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum cosmology, one exactly recovers isotropic loop quantum cosmology, including the usual ‘improved dynamics.’ We will also discuss how this reduction sheds light on which operator ordering to use when defining operators corresponding to directional Hubble rates, expansion, and shear – quantities relevant for discussing the resolution of the initial singularity.

Geometric constraint algorithm for field theories with boundaries.

Barbero F , Villase˜norE, Prieto J

The Loop Quantum Gravity treatment of black hole entropy rests on the description of black holes with the help of isolated horizons: inner spacetime boundaries where appropriate boundary conditions are imposed on the gravitational field. The implementation of the standard Dirac algorithm for field theories in the presence of boundaries is somewhat subtle and can lead to incorrect –or difficult to interpret– results. Fortunately there is an effective and geometrically appealing method to deal with this situation: the Gotay-Nester-Hinds geometric constraint algorithm. We discuss its implementation for scalar and electromagnetic fields defined in compact spatial manifolds with boundaries, discuss the implementation of the standard families of boundary condition and the interpretation of the resulting geometric description in terms of constraints. An important issue that we will consider in some detail is the precise characterization of the classical degrees of freedom.

Connection dynamics of a gauge theory of gravity coupled with matter

Banerjee K, Ma Y , Yang J

We consider the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing, which leads to a consistent geometrical dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints

221 can be solved, and a connection dynamical formalism of the theory can be obtained by a canonical transformation. Hence, the techniques of loop quantum gravity can be employed to quantize this Poincare gauge theory with non-zero torsion.

On loop quantization of plane gravitational waves

Major S, Hinterleitner F, Adelman J

Classically, spacetimes of plane gravitational waves with parallel rays may be obtained by a reduction of the polarized Gowdy model with the addition of a new constraint. This new constraint is diffeomorphism invariant in the symmetry reduced model. When expressed in terms of the new variables of loop quantum gravity, the system of constraints forms a first-class, but non-Lie, algebra. The eventual goal of the project is to investigate whether (and if so how) the apparent discreteness of spatial geometry in loop quantum gravity affects the propagation of gravitational waves. This talk focuses on the quantization of this model. Progress towards solving the constraints and identifying a space of Minkowski-type solutions will be discussed.

Loop quantum cosmology: fundamentals and phenomenology

Ashtekar A

We will review recent advances in our understanding of conceptual as well as observational issues related to the very early universe that have come from loop quantum cosmology. We will emphasize the interplay between the theory and observations has has the potential to enrich both areas.

An inflationary model in loop quantum cosmology

Fern´andez-M´endezM , Mena Marug´anG, Olmedo J

We present a complete quantization of an approximately homogeneous and isotropic universe minimally coupled to a massive scalar field with small scalar perturbations. Although the gauge is almost completely fixed before quantization, a gauge-invariant description can be attained in an appropriate fashion. The kinematical Hilbert space is constructed by combining the loop representation of the zero modes with a privileged Fock representation of the inhomogeneities. With a suitable prescription, the Hamiltonian constraint is promoted to an operator, whose solutions are characterized.

Duration of inflation as a prediction of effective lqc

Linsefors L, Barrau A

Loop quantum cosmology, together with a massive scalar field, has been shown to predict a high prob- ability of sufficiently long enough inflation to fit observations. However these predictions were derived from setting initial conditions at the bounce. In this study, we take seriously the direction of causality from past to future, and therefore set initial conditions before the bounce. The phase of the scalar field is assumed to be a random variable with a flat probability distribution. A key point of this distribution is that it is not linked to a specific point in time. Our result is independent of how long before the bounce we set the initial conditions, given reasonable assumptions. In this framework, we can show that the

222 number of e-folds of slow-roll inflation is peaked around N=145. This is one of the first clear theoretical prediction for the duration of inflation and it is also in agreement with observations. In addition, the fraction of potential energy at the bounce, usually taken as a free unknown parameter, driving many observable effects, can also be shown to be sharply peaked. Finally, we use those results to derive an original upper limit on the Barbero-Immirzi parameter : gamma ¡ 11, which is two orders of magnitude better than the previous limit coming from cosmology.

Quantum gravitational inflationary scenario in bianchi-i spacetime

Gupt B, Singh P

We study the inflationary scenario in Bianchi-I anisotropic spacetime in the effective description of loop quantum cosmology (LQC). We discuss the effects of the anisotropic shear and initial conditions on the amount of inflation, and also explore the differences between the evolution of classical and LQC Bianchi- I spacetime. We find that, unlike in the classical theory, the amount of inflation in LQC inflationary Bianchi-I spacetime does not vary monotonically with increasing shear. We also study the attractor behavior of the dynamical trajectories of Bianchi-I LQC spacetime. It turns out that the LQC trajectories show distinctly different attraction behavior than classical trajectories in the pre-inflationary era.

Qft on quantum spacetime

Dapor A

We develop a systematic classical framework to accommodate canonical quantization of both geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. It is shown that the existing approach of standard cosmological perturbations is good only (i) up to first order in the inho- mogeneities, and (ii) if the background is treated classically. A new set of classical phase space variables is proposed, which in a natural gauge define a complete and canonical algebra of relational Dirac ob- servables. We compute the physical Hamiltonian that generates the dynamics of such observavles (with respect to the homogeneous mode of a Klein-Gordon clock field), and offer a proposal for quantization: what we obtain is a theory of quantum perturbations on a quantum (cosmological) spacetime.

Introduction to quantum reduced loop gravity for cosmology

Cianfrani F

It is proposed the quantization of an inhomogeneous extension of the Bianchi I model as an arena to discuss the cosmological sector of Loop Quantum Gravity. The main features of reduced quantization are presented and it is outlined the failure of this approach to provide a sensible dynamics. This drawback is the motivation for introducing the framework of Quantum Reduced Loop Gravity, in which the order of reduction and quantization is reversed.

Quantum reduced loop gravity

Alesci E

We present a new framework to study symmetric sectors of loop quantum gravity: mimicking the spin- foam quantization procedure the reduction is imposed weakly on the full kinematical Hilbert space of

223 the canonical theory. As a first application we study the inhomogeneous Bianchi I model and discuss the semiclassical limit of the theory.

Asymptotic silence in quantum gravity

Mielczarek J

The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In par- ticular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counter- part at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density being of the order of the Planck energy density. At higher energy densities, the universe becomes 4D Euclidean space without causal structure. Therefore, the asymptotic silence appears to be an intermediate state of space between the Lorentzian and Euclidean phases. As we show, the observed signature change may be a result of spontaneous symmetry breaking, and the associated Goldstone boson is a natural candidate for inflaton.

Coherent state functional integrals in quantum cosmology

Qin L

Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models within the scheme of Gaussian coherent states. It turns out that for a nonsymmetric Hamiltonian constraint operator, the Moyal *-product emerges naturally in the effective Hamiltonian. This reveals the intrinsic relation among coherent state functional integral, effective theory, and Moyal *- product. Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit under certain condition.

Chimera: a hybrid numerical scheme for isotropic loop quantum cosmology

Diener P, Gupt B, Singh P

We extend the numerical investigations of isotropic loop quantum cosmology, sourced with massless scalar field, to more extreme initial conditions for which the volume at the bounce is of the order of a few Planck volumes, by considering widely spread semi-classical states. We probe the validity of effective dynamics for a wide variety of initial conditions, by comparing them with the LQC evolution of widely spread states. Numerical simulations of these states, due to the large computational domain, are computationally very expensive. Here we describe the numerical challenges and their remedies by introducing a hybrid numerical scheme, and present the results of simulations of states with a variety of initial conditions. We discuss physical consequences and viability of the effective description.

224 Qualitative effective dynamics in bianchi ix loop quantum cosmology

Corichi A, Karami A, Montoya E

We consider the issue of singularity resolution within loop quantum cosmology for the homogeneous and anisotropic Bianchi IX model. We show that the modifications which come from Loop Quantum Cosmology imply a non-chaotic effective behavior in the vacuum Bianchi IX model. Later, we present results of numerical evolutions of the effective equations. To address the issue of singularity resolution we examine the time evolution of geometrical and curvature invariants that yield information about the semiclassical spacetime geometry. Finally, We discuss generic behavior found for a variety of initial conditions.

Radiative corrections in covariant loop quantum gravity

Rovelli C

I explain the problem of the radiative corrections is covariant quantum gravity and summarize the present status of the research. The control of these radiative corrections is the main open issue in the theory.

Curvature constraints in spin foam models

Hellman F, Kaminski W

I will describe surprising constraints on the internal holonomies in the asymptotic limit of current spin foam models like EPRL. Our result concerns euclidean models but indicates that similar phenomena may occure also in their physical lorentzian counterpart.

Hamiltonian spinfoam gravity

Wieland W

The talk presents a new Hamiltonian formulation of discretised gravity, based upon the twistorial frame- work of loop quantum gravity. Within this framework, I am able to derive a continuum action adapted to a simplicial decomposition of space-time. The action is a sum of the spinorial analogue of the topo- logical ”BF” action and the reality conditions that guarantee the existence of a metric. The equations of motion admit a Hamiltonian formulation, that allows to perform the constraint analysis. I do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the re- ality conditions. With the action polynomial in the spinors, canonical quantisation is straightforward. Transition amplitudes reproduce the EPRL (Engle–Pereira–Rovelli–Livine) spinfoam model.

On the relation between canonical and covariant quantum gravity

Zipfel A

Heuristically, spin foams can be understood as the Feynman graphs of Quantum Gravity. Yet, summing over all ’histories’ would lead to a projector on the physical Hilbert space of the canonical theory rather

225 than to a true propagator due to the constraint nature of GR. Following this idea we construct a spin-foam operator acting on the kinematical Hilbert space and analyze its properties.

Observables in two-dimensional bf theory

Tavares S

Two dimensional BF theory has been a favourite subject of study in the last twenty five years. I will highlight how geometry played an essential part in the quantisation of this model and then expose how we are using the same fundamental view to calculate expectation values of operators. The key aspect will be introducing the mathematical model that allows us to treat surfaces with inbuilt ’topological defects’ and show how they relate to operators in the quantum field theory.

Asymptotic behaviour of lorentzian polyhedra propagator

Puchta J

A lorentzian polyhedra propagator T is an operator that appear in many spin-foam calculations. So far its behaviour was usually guessed by the analogy to corresponding object in the euclidean model. Recently its properties has been studied in details. The leading order of the propagator was found to be proportional to the identity operator. It is especially important to the calculation of the bubble divergence of the ’melonic graph’ radiative correction, which is proportional to logarithm of internal spin scale times T 2. Our result gives a way to renormalize this divergence.

The dipole cosmology transition amplitude: first-order contributions

Kisielowski M

Bianchi, Rovelli and Vidotto introduced Dipole Cosmology, a quantum cosmological model that opens a new theory which can be called Spin Foam Cosmology. In the original formulation they use a specific 2-complex. Its introduction was judged a posteriori by a correct semiclassical limit of the transition am- plitude. The 2-complex chosen has one internal vertex, and the calculation of a transition amplitude may be thought to be first-order calculations. In this talk we discuss other possible first-order contributions. We expect, that those contributions are dominated by the Bianchi-Rovelli-Vidotto transition amplitude in a limit of large volume of the universe, and a Spin Foam Cosmology model taking into account those contributions has a proper semiclassical limit.

Pentahedral volume, chaos, and quantum gravity

Haggard H

We show that chaotic classical dynamics associated to the volume of discrete grains of space leads to quantal spectra that are gapped between zero and nonzero volume. This strengthens the connection between spectral discreteness in the quantum geometry of gravity and tame ultraviolet behavior. We complete a detailed analysis of the geometry of a pentahedron, providing new insights into the volume operator and evidence of classical chaos in the dynamics it generates. These results reveal an unexplored realm of application for chaos in quantum gravity.

226 Poster session

A model hamiltonian for quantum isolated horizon

Majhi A

The Chern-Simons(CS) theory on the Isolated Horizon being a topological theory its Hamiltonian is zero. It is a constraint which generates gauge transformations on the IH. But the covariant phase space analysis shows that there is an energy function associated with the IH which satisfies a first law. This is an apparent self-contradiction of the IH theory which can probably be clarified from the quantum view point. The quantization of area in loop quantum gravity shows us a possible solution to this apparent contradiction. It is only at the quantum level that the IH get coupled to the bulk sources through the punctures which are the key building blocks of the Quantum IH(QIH). The punctures carry all the necessary ingredients of the theory and are responsible for the QIH area and should be responsible for the associated energy spectrum of the QIH. Motivated by Dirac’s theorem of commutating observables in elementary quantum mechanics I propose a model Hamiltonian for the QIH having a very general structure. The expectation values of the Hamiltonian operator and the area operator of the QIH are linearly related which, on taking variation, yields a first law on the IH. Also, as the model Hamiltonian commutes with the area operator, the expectation value of the area operator is a constant of motion indicating the non-expanding property of the IH. The commutation also indicates that they have the simultaneous eigenstates.

Polymer quantum matter in loop quantum cosmology.

Kreienbuehl A, Paw lowski T

The polymeric nature of quantum matter is studied using the example of a FLRW universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via deparametrization techniques, with the scale factor playing the role of time. Subsequently, the remaining dynamic degrees of freedom corresponding to the matter are polymer quantized. The analysis of the resulting genuine quantum dynamic shows that the big bang singularity is resolved, although with the form of the resolution differing significantly from that in the models with matter clocks: dynamically, the singularity is made passable rather than avoided. Furthermore, this analysis exposes crucial limitations to the so-called effective dynamic in loop quantum cosmology when applied outside of the most basic isotropic settings.

A kinematical quantum model for flat space

Hinterleitner F

An effectively 1+1 dimensional model for flat space is constructed from a system of plane gravitational waves by introducing null Killing vector fields that suppress the appearence of waves and thus guarantee flatness of space. The existence of these Killing fields is classically formulated in terms of first-class constraints. In a quantization procedure by means of one-dimensional spin networks ”no-wave solutions” of these constraints are constructed. Ambiguities in the formulation of the constraint operators are encountered, with some versions leading to diverging length and volume expectation values. In the result a two-parameter family of candidate states as solutions of different versions of the Killing constraints are obtained. Their main common features are different magnitudes of fluctuations of geometric quantities

227 and their rates of change. Application of the Hamiltonian constraint operator is in preparation with the aim to find out whether or not among this family of kinematical states there is a dynamical model of fluctuation flat space.

228 D2 - Strings, branes and M-theory

Oral session

Plasma dynamics and general relativity

Janik R

I will describe various developments in the applications of general relativity to the study of the dynamics of nonperturabtive plasma through the AdS/CFT correspondence. In particular I will describe numer- ical simulations corresponding to plasma equilibration as well as the relation of high order dissipative hydrodynamics with non-hydrodynamic quasi-normal modes.

A metric-like perspective on asymptotic symmetries in higher-spin gauge theories

Campoleoni A

We revisit the identification of the algebras of asymptotic symmetries of higher-spin gauge theories in three space-time dimensions. These models are usually described in terms of Chern-Simons theories, by adopting a formulation that generalizes the frame approach to gravity. A description closer to the metric approach to gravity, employing symmetric tensors in spite of differential forms, is however also possible. Following the latter approach we test the assumptions that one has to impose in the Chern-Simons formulation in order to recover non-linear W algebras of asymptotic symmetries.

Conical defects in higher spin gravity and minimal model holography

Raeymaekers J

I will present a class of smooth solutions in three-dimensional higher spin gravity, both in the Chern- Simons theories with sl(N) gauge symmetry and the Vasiliev theory with hs[ lambda] symmetry. These solutions can be interpreted as conical defects smoothened out by the higher spin fields. I will propose them to be holographically dual to specific states in minimal model CFT, and present evidence for this identification.

229 Scalars with higher derivatives in supergravity and cosmology

Koehn M , Lehners J, Ovrut B

We construct N=1 supergravity extensions of scalar field theories with higher-derivative kinetic terms. Special attention is paid to the auxiliary fields, whose elimination leads not only to corrections to the kinetic terms, but to new expressions for the potential energy as well. Our formalism allows one to write a supergravity extension of any higher-derivative scalar field theory and therefore has applications to both particle physics and cosmological model building. Our construction comprises the ghost condensate and galileon theories, which play an important role in non-singular bouncing cosmologies.

Monodromy transform and integral equation method for solving symmetry reduced string gravity and supergravity equations

Alekseev G

The monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for bosonic dynamics in string gravity and supergravity in four and higher dimensions. For physically different types of field configurations (stationary fields with spatial symmetries, interacting waves or partially inhomogeneous cosmological models) with interacting gravitational, dilaton, antisymmetric tensor and any number n of Abelian vector gauge fields (all depending only on two coordinates), the equivalent spectral prob- lem constructed earlier allows to parameterize the entire infinite-dimensional space of (normalized) local solutions by two pairs of coordinate-independent holomorphic (d x d)- and (d x n)- matrix functions of a spectral parameter. These functions constitute a complete set of monodromy data for normalized fundamental solution of this spectral problem. We construct the linear singular integral equations which allow to find the field configurations for any chosen monodromy data. For any rational and analytically matched monodromy data the solution of these integral equations can be found explicitly. Simple re- ductions of the space of monodromy data in 5D case leads to the similar construction for solving the integrable reductions of 5D minimal supergravity.

A positive energy theorem for the gravitational dirichlet problem

Kelly W , Marolf D

Gravity in the presence of a Dirichlet boundary condition (fixed metric on some time-like surface) has been extensively studied in the context of the AdS/CFT correspondence. We show that this system is stable in the sense that energy is bounded below by generalizing Witten’s proof of the positive energy theorem. Our proof applies to 3+1 dimensional spacetimes with vanishing cosmological constant, though we expect similar results to hold in higher dimensions and for negative cosmological constant. We also prove, under the same conditions, the familiar inequality M ≥ (Q2 + P 2)1/2, where M is the ADM mass and Q and P are the total electric and magnetic charge of the spacetime.

230 General relativity and superconductivity

Horowitz G

It has recently been shown that in addition to describing black holes, gravitational waves, and other gravitational phenomena, general relativity can also describe aspects of nongravitational physics including condensed matter. This is a result of a remarkable gauge/gravity duality that has emerged from string theory. I will explain this surprising development and illustrate it by showing how general relativity can reproduce aspects of superconductivity. It can even quantitatively reproduce novel aspects of the new high temperature superconductors.

Blackfolds, fluid/gravity and the membrane paradigm

Rangamani M

I will review the connections between the blackfold approach, the fluid/gravity correspondence, and the membrane paradigm. Using a simple example I will illustrate that the blackfold approach allows one to identify the low energy effective dynamics of black branes as fluid dynamics. Moreover, this blackfold construction encompasses the fluid/gravity correspondence formulated for asymptotically AdS spacetimes, and the membrane paradigm of black holes, and provides a universal framework to explore the dynamics of black objects in classical general relativity.

Black funnels

Way B, Santos J

The Hartle-Hawking state of N=4 SYM at strong coupling and large N on a fixed black hole background has two proposed gravitational duals: a black funnel or a black droplet. We construct the black funnel solutions that are dual to the Hartle-Hawking state on a Schwarzschild black hole and on a class of three- dimensional asymptotically flat black hole backgrounds. We compute their holographic stress tensor and argue for the stability of these solutions.

Wilson lines and entanglement in higher spin theories

Castro A, Ibqal N, Ammon M

Our goal is to construct the appropriate observable that will measure entanglement for higher spin gravity. The characteristic feature of these theories is the lack of a geometric interpretation of the fields beyond the perturbative level. The classical equations are formulated in a background independent way, and the gauge invariance is much larger than diffeomorphism invariance. Therefore we need to revisit simple geometric definitions that respect this enhanced gauge group. In this talk we will discuss how to construct a notion of a probe—with the aim to generalize geodesic distances—for higher spin theories. We will argue that the Wilson line is the correct probe of the geometry. It achieves the same goal as a geodesic for pure AdS gravity, in that the probe will report back a number which is the proper distance in the bulk. For higher spin gravity this topological probe gives new predictions in the context of AdS/CFT.

231 Geons and spin-2 condensates in the ads soliton

Hartnett G, Horowitz G

We construct geons starting with gravitational perturbations of the AdS soliton. Previous studies of a charged scalar field in the soliton background showed a holographic insulator/superconductor transition at a critical chemical potential. We explore the possibility that dimensional reduction of the geon could model a transition to a d-wave superconductor. We find that although one does get a charged spin- 2 condensate, it has higher free energy than the state without the condensate, so there is no phase transition.

Stringy structures of the 4d kerr geometry: n=2 superstring and calabi-yau twofold from the kerr theorem

Burinskii A

Gravitational background of the spinning particles corresponds to over-rotating 4d Kerr geometry, for which the Kerr singular ring is naked and forms a closed fundamental string of heterotic type. Complex Kerr geometry (in the Lind-Newman complex representation) is generated by a complex world-line which is equivalent to an open euclidean string. These two strings form together a string-membrane system, which is parallel to string/M-theory correspondence. Kerr theorem defines principal null congruence of the Kerr geometry. The related with complex string congruence is deskribed as a quartic in the projective twistor space, which corresponds to K3 surface embedded into real 4d Kerr geometry. We notice that structure of the complex source of the Kerr geometry is very similar to structures of the N=2 superstring, indicating that the complex N=2 superstring may be embedded in the complex Kerr geometry leading to a consistent 4d string theory.

Causal wedges in ads/cft

Hubeny V

The AdS/CFT correspondence has propelled AdS black holes into prominence as useful calculational tool in diverse branches of physics, but it also holds great potential for answering long-standing questions in quantum gravity by recasting them in non-gravitational language. The prereqisite for this program is good understanding of the dictionary between the two sides, which motivates the present exploration. We study the properties of a very natural gravitational construct – the causal wedge in AdS, pertaining to a specified spatial region on the AdS boundary – in order to obtain insight into its CFT dual. The construction is reminiscent of, but importantly distinct from, the correspondence between CFT entan- glement entropy and area of extremal surface in AdS (reviewed in the plenary talk by T. Takayanagi). After reviewing the causal wedge construction, we focus on interesting global properties of causal wedges in general time-dependent backgrounds.

Beyond symmetry in 3d higher spin holography

Perlmutter E

We present a collection of results supporting holographic dualities between 3D higher spin gravity and 2D higher spin-symmetric minimal model CFTs at large central charge, focusing particularly on those

232 that are not fixed by higher spin symmetry alone. This involves heating the duality to finite temperature and studying propagating matter in higher spin gravitational backgrounds. Holographic computations of boundary correlators, including some 4-point functions, provide a refined check of the duality as well as further insight into what constitutes a higher spin black hole.

Recurrence relations of kummer functions and regge string scattering amplitudes

Lee J

We discover an infinite number of recurrence relations among Regge string scattering amplitudes of dif- ferent string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decou- pling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.

Super-a-polynomials and 3-dimensional theories

Sulkowski P

In the last two decades it has been realized that intricate relations between knot theory, quantum field theory and string theory may be very fruitful, and taking advantage of them has led to several remark- able discoveries. In this talk I will introduce the notion of ”super-A-polynomials”, which form a new, intriguing family of algebraic curves. From mathematical viewpoint super-A-polynomials encode infor- mation about homological knot invariants. Physically they are related to a generalization (refinement) of 3-dimensional Chern-Simons theory with SL(2,C) gauge group, which is also known to be intimately related to 3-dimensional quantum gravity. On the other hand, from a certain dual perspective, each super-A-polynomial encodes information about 3-dimensional gauge theory with N=2 supersymmetry. These relations and dualities also shed a little light on a mysterious (2,0) superconformal theory of M5- branes. These topics are at the forefront of current research and lead to surprising new insights, which will be summarized in this talk.

On the horizon instability of an extreme reissner-nordstrom black hole

Murata K

Aretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner- Nordstrom black hole. We show that a similar instability occurs also for a massive scalar field. We present numerical results for the late time behaviour of massless and massive scalar fields in the extreme RN background and show that instabilities are present for initial perturbations supported outside the horizon, e.g. an ingoing wavepacket. We also study the nonlinear evolution of this instability in Einstein- Maxwell theory coupled to a massless scalar field, assuming spherical symmetry. We find that scalar field perturbations of an extreme Reissner-Nordstrom (RN) black hole generically exhibit an instability at the horizon but the solution eventually settles down to a non-extreme RN solution. However, there exist fine-tuned initial data for which the instability never decays. For such data, the ”endpoint” of the instability is a black hole which is extreme RN outside the horizon and has a curvature discontinuity at the horizon.

233 A Quantization Rule for Black Hole Horizons

Larsen F

Many black holes with multiple horizons satisfy a surprising quantization rule that involves the product of the areas for several horizons. The talk will describe the phenomenon through a few examples and also present an argument within classical GR that shows that this is a general rule for large classes of black holes.

234 Poster session

Quantum m-theory

Modesto L

We hereby present a class of higher derivative theories that realizes an ultraviolet completion of Einstein gravity. This class is marked by a non-polynomal entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high energy behaviour of the loop amplitudes. By power counting arguments, it is proved that the theory is (super-)renormalizable in even dimension and “finite” in odd dimension. Comparing these theories with superstring theory and string field theories, a unique form factor is singled out. In view of this, we can modify the 10-dimensional supergravity and finally get a ultraviolet completion of 11-dimensional supergravity by an “oxidation process”. The result is a finite “Quantum M-theory”.

Cosmic strings in 5d

Slagter R

Cosmic strings occur as topological defects, consisting of confined regions of false vacuum energy in gauge theories with spontaneous symmetry breaking in the early stages of the universe. They could have served as seeds for the formation of the large scale structure of the galaxies and clusters and predict axially symmetric gravitational lensing effects. However, observations of the CBR, would rule out these effects. Apart from their possible astrophysical role, they are fascinating objects in their own right and can give rise to a rich variety of unusual physical phenomena such as the (2+1)-dimensional spinning point particles, which could admit closed timelike curves. The appearance of the so called Gott spacetime, in which an advanced civilization could produce a closed timelike curve, turns out to induce tachyonic behavior. An uprising of the cosmic string investigations occurred after it was realized that M-theory, the improved version of superstring theory, allows, via brane world scenarios, macroscopic fundamental stings that could play a role very similar to that of cosmic stings. If one investigate the behavior of self gravitating gauge cosmic strings in a warped 5-dimensional spacetime, where the extra dimension can be as large as 10-3cm, the Gott condition could be fulfilled in order to get closed timelike curves. Moreover, in these warped spacetimes, the behavior of cosmic strings changes dramatically and could resolve the observational conflicts.

Some aspects of brany kerr spacetimes relevant to accretion processes

Blaschke M , Stuchl´ıkZ

We consider equatorial motion of test particles around rotating Kerr naked singularity in the Randall- Sundrum braneworld scenario and its implications for the properties of Keplerian accretion disks. We demonstrate existence of some unexpected phenomena related to properties of spacetimes having positive braneworld tidal charges.

235 D3 - Causal sets, causal dynamical triangulations, non-commutative geometry, and other approaches to quantum gravity

Oral session

Causal dynamical triangulations without preferred foliation

Loll R, Jordan S

We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quan- tum gravity, in which the regularized, triangulated path integral histories maintain their causal proper- ties, but do not have a preferred proper-time foliation. An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity. This suggests that the preferred foliation normally used in CDT is not a crucial (although convenient) part of its background structure.

The effective action in 4-dim cdt (the transfer matrix approach).

Gizbert-Studnicki J , Jurkiewicz J, Ambjorn J, Gorlich A

The Causal Dynamical Triangulations (CDT) model is a non-perturbative path integral approach to quantum gravity. In four dimensions it was successful in spontaneously generating quantum fluctuations of the scale factor of the universe around the semi-classical de Sitter solution. There is evidence that fluctuations are governed by the effective action being a discretization of the mini-superspace action. The form and the parameters of the action could be accessed indirectly by the measurement of the covariance matrix of volume fluctuations. We propose a new way to measure the effective action directly. This is done by introducing a simple fenomenological transfer matrix whose elements are labeled by the scale factor. The transfer matrix can be measured in Monte Carlo simulations. By a direct measurement we examine the properties of the effective action inside the ”C” (de Sitter) phase of CDT. We show that the mini-superspace action is valid not only in the large volume range but also in the small volume limit where discretization effects are strong. We compare the parameters of the effective action measured directly with those measured indirectly in our previous work. We also examine the properties of the CDT effective action in other phases (”A” and ”B”).

236 Asymptotic safety and the non-perturbative renormalization group flow of f(r)-gravity

Zanusso O

We review the non-perturbative renormalization group flow of f(R)-gravity and describe its implications in constructing a finite and predictive theory of quantum gravity thorough the Asymptotic Safety program. We will also present the analytical and numerical techniques developed in the process of analyzing the flow.

Unimodularity and ghosts in asymptotically safe quantum gravity

Eichhorn A

I will briefly review the main idea behind asymptotic safety, before discussing some new results on the program: I will point out that there could be several inequivalent versions of asymptotically safe quantum gravity: In fact, besides the standard formulation, a unimodular version of gravity also shows a nontrivial fixed point within a first truncation of the Renormalization Group flow. Then I will focus on the standard formulation of asymptotic safety, and discuss its Faddeev-Popov ghost sector. In the far ultraviolet, this develops surprising new features, which are crucially different from a perturbative setting, and can be rather challenging to interpret.

Time as a transitive relation

Rideout D

A natural, covariant way to regard the familiar notion of coordinate time is as a linear extension of the binary relation which encodes causal structure. Binary relations are well studied in a variety of contexts, however the imposition of transitivity turns out to have important and relatively poorly understood implications. In particular, we formulate a simple theory of quantum cosmology in terms of a finite transitive partial order, in which a quantum amplitude exp(iS) is associated to each finite universe. The action S is formulated as a discrete analog to the Einstein-Hilbert action for gravity, defined on finite partial orders. The implications of the theory are explored by Metropolis Monte Carlo. The results reveal a surprising richness to the structure of finite transitive relations, and also indicate a regime which, when performing the sum over the set of all finite transitive relations of fixed cardinality, has the potential to produce universes of non-trivial temporal extent and finite dimension.

Towards locality in causal sets

Glaser L, Surya S

In Causal Set Quantum Gravity it is very difficult to define what a local neighborhood should be. This is one of the big problems in practically recovering the structure of the manifold from the causal set. In this talk I will present some work on a new observable in causal sets which can be used to define a local neighborhood. We found that the number of intervals that contain a given number of elements follows a very specific distribution. This distribution is dependent on the dimension and curvature of spacetime. These so called interval abundances can be calculated analytically and the results agree with

237 simulations. We thus fund a new way to measure manifoldness and dimension in a causal set. The same observable can also be used to define a local neighborhood of a point.

Causal set dynamics: results in 2d quantum gravity

Surya S

We use Markov Chain Monte Carlo methods to generate a quantum dynamics for a 2D model of causal set quantum gravity. Our results show that 2D flat spacetime is emergent from the dynamics in a certain parameter and large temperature regime. In the low temperature regime, the dominant causal sets are however non-manifoldlike, being ”crystalline” in character. There is a cross-over between these two regimes and we examine the features of this cross-over using a set of covariant observables. Impor- tantly, the continuum phase being close to the infinite temperature line appears to survive the analytic continuation.

Kinematic quantum states for the teleparallel equivalent of general relativity

Okol´owA

A space of kinematic quantum states for the Teleparallel Equivalent of General Relativity is constructed by means of projective techniques. The states are kinematic in this sense that their construction bases merely on the structure of the phase space of the theory and does not take into account constraints on it. The space of quantum states is meant to serve as an element of a canonical quantization of the theory.

The continuum limit of spin foams and spin nets

Dittrich B

Spin foam models are candidate models for quantum gravity, constructed via a quantum mechanical (not Wick rotated) path integral for discrete gravity. We aim to extract the behaviour of these models on scales large compared to the discretization scale. To this end we employ recently introduced coarse graining techniques, known as tensor network renor- malization methods, that allow us to obtain a renormalization flow of these models. Fixed points of this flow correspond to the infinite refinement, that is continuum, limit. These techniques are applied to dimensionally reduced models, which we coined spin net models. However important general mechanisms can be already studied for these reduced models and we will comment on these as well as on general strategies for renormalization in background independent systems.

Fuzzy space-time topology, quantization and gauge fields

Mayburov S

Dodson-Zeeman fuzzy topology (FT) is studied as possible basis of quantum space-time geometry. As the example, quantization of massive particle m is analyzed. In FT the fundamental set of elements (points) S is Poset, so that its elements (points) beside standard ordering relation bleq c, can obey also to incomparability relation : b c, . To detalize it, the normalized fuzzy weight w(b, c) > 0 is

238 introduced. If X is continuous ordered S subset, and for some range of its elements x : b x, then b coordinate relative to X can be principally uncertain, w(b,x) characterizes its spread. It supposed that b(t) describes particle m, assuming S space-time shift invariance it’s shown that m state ϕ(t) obeys to Dirac equation. Possible FT structures of Lorentz-covariant noncommutative spaces are considered. Particle’s interactions on fuzzy manifold are found to be gauge invariant, for fermions they are performed by corresponding Yang-Mills fields.

Renormalization group flow in cdt quantum gravity

Ambjorn J

Causal dynamical triangulations (CDT) provide a lattice regularization of quantum gravity. Using the (discretized) Einstein-Hilbert action, the phase diagram of the lattice theory has three phases and a Lifshitz-like structure with a tripple point where the three phases meet. The renormalization group flow of the bare lattice coupling constants is followed along lines of constant physics. In this way the lattice approach is connected to the asymptotic safety scenario. The phase diagram has a second order phase transition line and when one is close to this phase transition line the lines of constant physics move towards the triple point. Properties of the tenative continuum quantum gravity theories obtained by approaching the second order phase transition line are discussed, including a discussion of the symmetry between space and time which cannot be taken for granted in the CDT approach, which shares many features with Horava-Lifshitz gravity.

2d cdt is 2d horava-lifshitz quantum gravity

Glaser L, Ambjorn J, Sato Y, Watabiki Y

Causal Dynamical Triangulations (CDT) is an approach to quantum gravity which attempts to regularize the path integral of gravity by discretizing the manifold. This approach allows for analytic work in 2 dimensions and Monte Carlo simulations in higher dimensions. CDT is not a fundamentally discrete approach since the goal is to take the continuum limit at the end of calculations. In this way the analytic work has led to an effective Hamiltonian for the quantum theory. However so far it has not been possible to directly connect the quantum theory of CDT to any classical theory. Horava Lifshitz gravity is a proposed modification of general relativity which is perturbatively renormalizable. Both Horava Lifshitz gravity and CDT require a preferred foliation of space time, so it has been proposed that CDT might be a quantum theory for Horava Lifshitz gravity. In this talk I will present recent work on connecting CDT to the classical theory of Horava Lifshitz gravity. I will show how to obtain the effective 2d CDT Hamiltonian through canonical quantization of 2d Horava-Lifshitz gravity.

Phase structure of 4d edt with a measure term

Gorlich A

We present recent results obtained for four-dimensional Euclidean Dynamical Triangulations with a local measure term. We study the phase diagram of this model using non-degenerated triangulations and show that there is no evidence of a new extended phase.

239 Precanonical quantization of vielbein gravity and the classical limit

kanatchikov I

Precanonical quantization is based on the De Donder-Weyl Hamiltonian formulation, which requires no splitting into space and time and no infinite dimensional spaces of field configurations. The standard functional Schroedinger representation of QFT can be obtained from precanonical quantization in the limiting case of the vanishing parameter 1/κ of the latter which has a meaning of the minimal volume scale. We use the approach developed in our previous papers to quantization of the first-order vielbein gravity. We derive the operator representation of vielbeins and metric tensor in terms of differential operators on the space of spin connections and a covariant analogue of the Schroedinger equation on the bundle of spin-connection coefficients over space-time. Quantum geometry of space-time is described in terms of the transition amplitudes on the latter. We define the indefinite metric Hilbert space of the theory and the invariant measure on the space of spin connection coefficients, and show how the evolution of the expectation values of spin-connection and vielbein operators matches the Einstein equations as a consequence of quantum evolution given by the covariant Schroedinger equation derived from precanon- ical quantization. We also discuss an application to quantum cosmology and the relation between the value of the cosmological constant predicted by the approach and that of the parameter κ of precanonical quantization.

Spacetime fuzziness and the pregeometry of kappa-minkowski

Rosati G

Several approaches to the quantum-gravity problem suggest that spacetime should become ”fuzzy” at the Planck scale. We here provide a physical characterization of spacetime fuzziness derived constructively within the quantum picture of spacetime provided by kappa-Minkowski noncommutativity. Our con- struction rely on a ”pregeometric” representation of both kappa-Minkowski coordinates, kappa-Poincar´e symmetry generators and of their associated differential calculus. The relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, while the dynamics takes place in the ”physical Hilbert space” after enforcing the Hamiltonian constraint. In this formulation spacetime points are ”fuzzy”, while particles motion is described by ”fuzzy worldlines”.

Generalized deformed poincare algebras

Pachol A

Deformation of Poincare algebra within the Hopf algebra language introduces the deformed symmetry for noncommutative spacetimes. Noncommutative spacetimes with their deformed symmetries constitute to one of the approaches for the description of Planck scale physics. One of the possible assumptions is that below Planck scale spacetime has more general structure, a noncommutative one where (as with quantum mechanics phase-space) uncertainty relations naturally arise. In my talk I will present the generalized description for the kappa-deformed Poincare Hopf algebra compatible with the kappa- Minkowski spacetime. For the given realization of kappa-Minkowski spacetime there exists a unique kappa-Poincare Hopf algebra with undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra will be shown as special cases. Moreover deformations of symmetry algebras of spacetime also appear in loop quantum gravity approach. And one of the generalized Poincare algebras seems to be in agreement with the hypersurface deformation algebra found recently.

240 Fedosov quantization and geometric non-commutative deformations of general relativity

Dobrski M

Pure geometric, non-commutative deformations of vacuum gravity, corresponding to an arbitrary sym- plectic non-commutativity tensor can be constructed within Fedosov formalism of deformation quan- tization of endomorphism bundle. Such approach allows derivation of fully coordinate covariant field equations and computation of their solutions (corrections to an arbitrary Ricci-flat metric up to the second order of the deformation parameter). The resulting model can be shown to be strongly related to the theories based on the Seiberg-Witten map.

Tunneling during quantum collapse in ads spacetime

Vaz C, Lochan K

We will discuss the tunneling mechanism through the apparent horizon in the LTB dust collapse sce- nario in the Wheeler DeWitt dust collapse scenario. We will discuss the results on the reflection and transmission of dust shells across the apparent horizon during quantum collapse of the non-marginally- bound dust in arbitrary dimensions with a negative cosmological constant. We will discuss the thermal radiation profile owing to the singular structure of the Hamiltonian constraint at the apparent horizon and try to compare with different schemes of quantization. We show that the Hawking temperature is independent of the energy function and that the wave functional describing the collapse is well behaved at the Hawking-Page transition point.

An algebraic formulation of causality for noncommutative geometry

Eckstein M

Noncommutative Geometry a la Connes offers a vast generalisation of Riemannian geometry with direct applications to physics. A description of Lorentzian manifolds in this framework is also possible, leading to the notion of a Lorentzian Spectral Triple. After presenting the necessary rudiments, I shall propose an algebraic formulation of the notion of causality for spectral triples corresponding to globally hyperbolic manifolds with a well defined noncommutative generalization. The talk is based on joint work with Nicolas Franco (Copernicus Center, Krak´ow).

241 Poster session

Does temperature quenching in the early universe exist in part due to particle production? or quantum occupation states

Beckwith A

We examine the role of particle nucleation in the initial universe, and argue that there is a small effect due to particle nucleation in terms of lowering initial temperature, in tandem with energy density and scale factor contribution. If such scaling exists as a major order effect, then quenching of temperature proportional to a vacuum nucleation at or before the electroweak era is heavily influenced by a number, n, which is either a quantum number (quantum cosmology) or a ’particle count at/before the electro weak era. Gravitons/gravitino production in the early universe may shed light as to what the number n is

Discrete symmetries as the origin of the lorentz group

Kerner R

The Lorentz invariance was first introduced as a symmetry concerning the classical field theory and the averaged macroscopic quantities such as electric and magnetic fields. Later on it was extended to quantum objects, represented by non-commuting operators. It also turned out that the symmetry underlying the Lorentz group was in that case the SL(2,C) group. We present a point of view that this group appears naturally if we require the invariance of two postulates, the Pauli exclusion principle and the superposition principle. Then we extend Pauli’s principle to a Z-3 graded case and show how a non-linear representation of the SL(2,C)xZ3 group appears as a natural symmetry for the quark states.

Generalized uncertainty principles, convexity and the pythagorean metric of space(-time)

Kalogeropoulos N

Motivated by proposed generalised uncertainty principles, that have attracted considerable attention during the last two decades, we address the question of why space(-time) has a metric obeying the Pythagorean theorem (l2). We propose to look into the matter from the viewpoint of convexity as quan- tified through the modulus of convexity. All Riemannian manifolds (space-times) are locally Euclidean spaces, so we work in the context of Rn, since we are interested in the short distance (”ultraviolet”) properties of space(-time). Following the approach encountered the algebraic quantum field theories and non-commutative geometry, we work with appropriate spaces of functions on Rn encoding its structure, rather than with Rn itself. The simplest class of such spaces are the Lebesgue spaces of functions (Lp) on Rn. Hanner’s inequalities imply that the Hilbert spaces (L2) have the largest moduli of convexity among all Lp (Rn), hence they are the desirable spaces, from our convexity viewpoint. We ponder on the possible physical explanation that may motivate and lie behind such considerations of convexity, relying on some of its occurrences in General Relativity, Statistical Mechanics, Geometry and Optimal Transportation.

242 D4 - Quantum fields in curved space-time, semiclassical gravity, quantum gravity phenomenology, and analog models

Oral session

On the algebraic quantization of abelian gauge theories on curved spacetimes

Dappiaggi C

Abelian gauge theories on a generic globally hyperbolic spacetime are best formulated as theories for connections on non trivial principal bundles. Their quantization is discussed within the framework of algebraic quantum field theory and particular emphasis is given to the structure and to the role of the gauge group. As a byproduct of our analysis, we will show that these theories do not abide to the principle of general local covariance. The reason for such a failure can be ascribed to the presence of non local features, which, in the case of electromagnetism, arise from Gauss law.

Supersymmetric quantum gauge field theories in curved spacetime

Hollands S

Supersymmetric quantum gauge field theories are normally considered on Minkowski spacetime. How- ever, there exists a procedure to put such theories on a curved spacetime if the background is geometrically special, in the sense that it admits certain types of spinor fields, called ”twistor spinors”. These are the generators of the fermionic symmetry. We show that in this case, the standard N=2 supersymmetric gauge theories in d=4 can be put on such spacetimes. We then ask when these symmetries are preserved at the quantum level. Using a cohomological method combined with techniques of renormalization the- ory on curved spaces, we give a characterization of the class of spacetimes/gauge groups/representations for which the supersymmetries are realized at the quantum level. Our analysis also leads to interesting conclusions for those spacetimes which do not admit twistor spinors, but conformal symmetries. It is found that typically, the group of conformal transformations is broken to a discrete subgroup at the quantum level.

243 A perturbative de sitter s-matrix

Marolf D, Morrison I, Srednicki M

We introduce a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski- space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem.

The de sitter s-matrix of the principal chiral model

Morrison I

We construct the exact scattering matrix of the Principal Chiral Model (PCM) in 2-dimensional global de Sitter spacetime. The PCM is an intriguing theory: it is an integrable, interacting non-linear sigma model exhibiting asymptotic freedom and dimensional transmutation. At weak coupling the PCM describes massless degrees of freedom whose description on an expanding spacetime could naively suffer from crippling infrared divergences on an expanding spacetime. However, using bootstrap techniques as well as scattering techniques specific to de Sitter spacetime we determine the scattering matrix, modulo the usual CCD ambiguity. The flat-space limit of this de Sitter S-matrix agrees with the known exact S-matrix of the PCM on Minkowki space.

Quantum-correcting electromagnetism on de sitter

Woodard R, Degueldre H

Inflation rips virtual gravitons and massless, minimally scalar out of the vacuum. When such a scalar is charged the resulting vacuum polarization induces a profound change in electromagnetism. I describe how this can be explored, and I present results for the fields induced by point charges and point magnetic dipoles.

On the existence of hartle-hawking-israel states on static black hole spacetimes.

Sanders K

The discovery of black hole radiation (Hawking, 1975) was soon followed by the conjecture that a free scalar quantum field on a Schwarzschild black hole admits a unique ground state, which restricts to a thermal state at the Hawking temperature in the exterior region (Hartle and Hawking, 1976; Israel, 1976). This conjecture was later extended to more general static black holes (Jacobson, 1994) and the state is known as the Hartle-Hawking-Israel state (HHI-state).

244 Since 1975, the study of quantum fields in curved spacetimes has made much progress, but a full proof of the conjecture on the HHI-state has remained elusive. Partial results include the construction of such a state in the exterior regions of a stationary black hole (Kay, 1985) and the landmark result that the HHI-state is the unique stationary state on a stationary black hole which is Hadamard even across the black hole horizon (Kay and Wald, 1991; Kay 1993). There is also a sketched proof of the existence of a Euclidean counterpart of the HHI-state in static black holes (Jacobson, 1994). We will present the state of the art results on the existence of the HHI-state on a class of static black holes. Using a Wick rotation and the Euclidean HHI-state we arrive at a putative two-point distribution on the black hole spacetime, which is of Hadamard type, has the correct antisymmetric part and extends the HHI-state of (Kay, 1985) in the exterior regions. Whether it is of positive type is still under investigation.

Tunneling processes through black hole horizons and hawking radiation

Pinamonti N

The interplay of tunneling processes through black hole horizons and Hawking radiation has recently been investigated in a first quantization scheme. During this talk we shall discuss the same issue in the realm of quantum field theory on curved spacetime. We shall show that the correlation functions of a quantum scalar field theory appear to have thermal nature when the scaling limit towards the horizon of the two-point function of a large class of states is considered. Since the computation is completely local the analysis covers also the case of horizons which exit only for small amounts of time, giving thus a strong support to the idea that the Hawing radiation is actually related to some local phenomenon. Some comments about the case of self-interacting fields will also be given.

Accelerated cavities at relativistic velocities

Bruschi D, Louko J , Fuentes I, Faccio D

We address quantum fields in an accelerated cavity in (3+1)-dimensional Minkowski spacetime in a per- turbative formalism that assumes acceleration to remain small but allows the velocities, travel times and travel distances to be arbitrary, and remains in particular valid when the velocities become relativistic. The formalism is well suited for analysing the effects of acceleration on quantum information protocols, and it generalises to analogue systems that simulate mechanical cavity motion. As an application, we we identify a desktop experimental scenario where mode mixing within the cavity appears to be at the threshold of current technology.

Negative energy seen by accelerated observers

Roman T

The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The quantum inequalities severely limit the utilization of negative energy to produce gross macroscopic effects, such as violations of the second law of thermodynamics. The restrictions on the sampled energy density along the worldlines of accelerated observers are much weaker than for inertial observers. We consider the worldline of a particle undergoing sinusoidal motion in space in the presence of a single mode squeezed vacuum state of the electromagnetic field. We show that it is possible for the integrated energy density along such a worldline to become arbitrarily negative at a constant average rate. This can be the case even when the particle moves at non-relativistic speeds. The the Raychaudhuri

245 equation is used to show that there can be net defocusing of a congruence of these accelerated worldlines. This defocusing is an operational signature of the negative integrated energy density. These results in no way invalidate nor undermine either the validity or utility of the quantum inequalities for inertial observers. In particular, they do not change previous constraints on the production of macroscopic effects with negative energy, e.g., the maintenance of traversable wormholes.

Probability distributions for quantum stress tensor fluctuations

Ford L, Fewster C, Roman T

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function in time, in the four-dimensional Minkowski vacuum. Of particular physical interest is the energy density of the quantized electromagnetic field. The probability distribution for vacuum fluctuations has a negative lower bound, which coincides with the quantum inequality bound on time-averaged expectation values in any quantum state. This lower bound can be understood as the lowest eigenvalue of the time- averaged energy density operator. We approach the problem of constructing the probability distribution by explicit calculation of the first 65 moments. We find that these moments grow too fast for the probability distribution to be uniquely determined by its moments. Nonetheless, some general features, such as the lower bound and the asymptotic form of the distribution for large argument, should be given by our set of moments. This asymptotic form is of special interest: we find that it falls as a power times an exponential of minus the one-third power of the sampled energy density. Thus it falls more slowly than does the Boltzmann distribution. This result has the interesting consequence that at a sufficiently high energy scale, vacuum fluctuations will always dominate thermal fluctuations. We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

Primordial fluctuations induced by quantum stress-energy fluctuations

Siemssen D

In a seminal paper Sachs and Wolfe predicted temperature anisotropies in the CMB only shortly after its discovery by Penzias and Wilson. Modern cosmological experiments like WMAP have observed and quantified these anisotropies and found them to be consistent with nearly scale-invariant gravitational perturbances at the time of decoupling. In the inflationary paradigm it is believed that quantum fluctua- tions during inflation seeded these perturbations. In this talk I will present an extension of the semiclas- sical Einstein equations which couples n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. Taking as a model a massive conformally coupled scalar field on a perturbed de Sitter space in a generic Hadamard state, I will describe how a scale- invariant power spectrum is produced independent of any direct renormalization effects. Furthermore, I will discuss how this model yields a natural basis for the calculation of non-Gaussianities.

What happens when a freely-falling observer crosses an event horizon–semiclassically?

Smerlak M

What happens when a freely-falling observer crosses a black hole horizon? In spite of recent challenges by Almheiri, Marolf, Polchinski and Scully—the ”firewall” hypothesis—, the consensual answer to this question tends to remain ”nothing special”. In this talk, I will show that something rather special

246 happens near the horizon, already at the semiclassical level: particle detectors record ingoing Hawking radiation at a temperature inversely proportional to their velocity relative to the horizon. To establish this result, I will (i) introduce an adiabatic expansion for Unruh-DeWitt response functions along non- stationary trajectories, and apply it to radial Schwarzschild geodesics, and (ii) compute the flux perceived by such infalling observers. I will close with a few comments on the role of spacetime curvature in this surprising effect.

Death and resurrection of the zeroth principle of thermodynamics

Haggard H , Rovelli C

The zeroth principle of thermodynamics in the form ”temperature is uniform at equilibrium” is notori- ously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the gen- eral context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the tem- perature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.

Thermodynamics of a black hole with moon

Gralla S, Le Tiec A

For a rotating black hole perturbed by a particle on the ”corotating” circular orbit (angular velocity equal to that of the event horizon), the black hole remains in equilibrium in the sense that the perturbed event horizon is a Killing horizon of the helical Killing field. The associated surface gravity is constant over the horizon and should correspond to the physical Hawking temperature. We calculate the perturbation in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also compute the surface area/entropy, and find no change from the background Kerr value.

Clausius entropy for arbitrary bifurcate null surfaces

Baccetti V , Visser M

The ontological reality of entropy is still a matter of heated debate. Indeed, part of the issue is due to the existence of several definitions of entropy and to the extent to which they can be considered equivalent. A consensus opinion is that Clausius entropy should be objectively real, while the ontological status of the statistical entropy is much more likely to be observer-dependent. This question becomes particularly important when considering Jacobson’s ”thermodynamic” derivation of the Einstein equations, where, on the one hand, an entanglement entropy interpretation of Bekenstein entropy is consider, while on the other hand, the thermodynamic concept of Clausius entropy is applied to local Rindler horizons. In this talk we will address this point and show that one can meaningfully assign a notion of Clausius entropy to matter crossing arbitrary bifurcate null surfaces. In particular, since any null surface can be considered as an observer-dependent causal horizon, its associated Clausius entropy can be defined as observer-dependent as well, a result that undermines the ontological reality of Clausius entropy.

247 Extremal versus non-extremal black hole entropy: a thermodynamic approach

Lemos J, Quinta G, Zaslavskii O

Black hole entropy S is one of the most fascinating issues in contemporary physics, as one does not yet know what are the degrees of freedom at the fundamental microlevel. In addition, there are two mutually inconsistent results for extremal black holes. There is the usual S = A/4 value, where A is the horizon radius, obtained from string theory [1], and there is the prescription S = 0 obtained from the fact that for extremal black holes the period of the Euclidean time is not fixed in a classical calculation of the action [2]. In order to better understand this problem, we exploit a framework set up by Martinez [3] and use a thermodynamic approach for an electrically charged thin shell. We then take the shell radius into its horizon limit (see also [4]). This limit is called a quasiblack hole. We show that (i) for a non-extremal shell the horizon limit yields S=A/4, and (ii) for an extremal shell the horizon limit gives an entropy which is a function of the horizon radius alone, but the precise functional form depends on how we set the initial shell. This formalism clearly shows that non-extremal and extremal black holes are different objects. [1] A. Strominger, C. Vafa, Phys. Lett. B 379, 99 (1996); arXiv:hep-th/9601029. [2] C. Teitelboim, Phys. Rev. D 51, 4315 (1995); arXiv:hep-th/9410103. [3] E. A. Martinez, Phys. Rev. D 53, 7062 (1996). [4] J. P. S. Lemos, O. B. Zaslavskii, Phys. Lett. B 695, 37 (2011); arXiv:1011.2768 [gr-qc].

Quantum resolution of timelike singularities in spherically symmetric, conformally static spacetimes

Konkowski D, Helliwell T

Following pioneering work by Wald, a proposal for using quantum fields to resolve singularities in static spacetimes with timelike singularities was originated by Horowitz and Marolf. A static spacetime is termed quantum mechanically non-singular if the spatial portion of the relevant wave operator is essen- tially self-adjoint in the space of square-integrable functions on a spatial slice. We have shown that the Horowitz and Marolf definition of quantum non-singularity for static spacetimes can be extended to the case of conformally static spacetimes. We have tested the formalism for a class of conformally static, spherically symmetric spacetimes, a class that includes the special cases studied by Roberts, by Fonarev, and by Husain, Martinez and N´u´nez.We use as quantum fields the solutions of the generally coupled, massless Klein-Gordon equation, and Weyl’s limit point - limit circle criteria for judging the existence of quantum singularities. This requires that we write the radial part of the Klein-Gordon equation in the form of a one-dimensional Schr¨odingerequation, and evaluate the behavior of the associated potential energy in the vicinity of the singularity. In this way we discover the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are resolved quantum mechanically.

Equality between gravitational and electromagnetic absorption cross sections of extreme reissner-nordstrom black holes

Crispino L, Oliveira E, Higuchi A

The absorption cross section of Reissner-Nordstrom black holes for the gravitational field is computed numerically, taking into account the coupling of the electromagnetic and gravitational perturbations. Our results are in excellent agreement with low- and high-frequency approximations. We find equality between gravitational and electromagnetic absorption cross sections of extreme Reissner-Nordstrom black

248 holes for all frequencies, which we explain analytically. This gives the first example of objects in general relativity in four dimensions that absorb the electromagnetic and gravitational waves in exactly the same way.

Inflationary cosmological backreaction and test field observers.

Marozzi G

In an inhomogeneous universe, an observer associated with a particular matter field does not necessarily measure the same cosmological evolution as an observer in a homogeneous and isotropic universe. In this talk, I will consider, in the context of a chaotic inflationary background model, a class of observers associated with a ”clock field” for which I will use a light test field. The computation of the effective expansion rate and fluid equation of state is then presented in a gauge invariant way, taking into account the quantum fluctuations of the long wavelength modes, and working up to second order in perturbation theory and in the slow-roll approximation. To conclude, I will show how the effective expansion rate is smaller than what would be measured in the absence of fluctuations.

Kermions

Winstanley E

We study the construction of quantum states on a non-extremal Kerr black hole. For a bosonic quantum field, it is known that no analogues of the Boulware and Hartle-Hawking states can be constructed. For a fermionic quantum field, we will define a candidate ‘Boulware’-like state, empty at both past and future null infinity; and a candidate ‘Hartle-Hawking’-like state, representing a thermal bath of fermions surrounding the black hole. Neither of these candidate states have analogues for bosons on a non-extremal Kerr black hole. Both have physically attractive regularity properties.

Time dependence of particle creation from accelerating mirrors

Good M , Evans C, Anderson P

Particle production due to a quantized, massless, minimally coupled scalar field in two-dimensional flat spacetime with an accelerating mirror is investigated, with a focus on the time dependence of the process. We analyze first the classes of trajectories previously investigated by Carlitz and Willey and by Walker and Davies. We then analyze four new classes of trajectories, all of which can be expressed analytically and for which several ancillary properties can be derived analytically. The time dependence is investigated through the use of wave packets for the modes of the quantized field that are in the out vacuum state. It is shown for most of the trajectories studied that good time resolution of the particle production process can be obtained.

High-temperature expansion of the one-loop free energy of a scalar field on a curved background

Kalinichenko I

The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent

249 and finite parts of the high-temperature expansion in a three-dimensional space without boundaries are obtained. These formulas generalize the known one for the stationary spacetime. In particular, we confirm that for a massless conformal scalar field the leading correction to the Planck law proportional to the temperature squared turns out to be nonzero due to the nonstatic nature of the metric. The explicit expression for the so-called energy-time anomaly is found. The interrelation between this anomaly and the conformal (trace) anomaly is established. The natural simplest Lagrangian for the ”Killing vector field” is given.

Multimessenger quantum-spacetime astrophysics

Amelino-Camelia G

Part of the quantum-gravity community had ben waiting for the start of data taking by the Fermi gamma-ray telescope and the IceCube neutrino telescope. These telescopes have now accumulated a few years of data and I observe that their findings impose that we reshape some aspects of the relevant quantum-spacetime phenomenology.

Upper limit on possible planck-scale modifications on the ground-state energy of the gw detector auriga

Cerdonio M , Marin F, Marino F, Bonaldi M, Conti L, Falferi P, Mezzena R, Ortolan A, Prodi G, Taffarello L, Vedovato G, Vinante A, Zendri J

Different approaches to quantum gravity, such as string theory and loop quantum gravity, as well as doubly special relativity and gedanken experiments in black-hole physics, all indicate the existence of a minimal measurable scale, of the order of the Planck length, Lp = 1.6 × 10−35 m. This observation has motivated the proposal of generalized uncertainty relations, which imply changes in the energy spectrum of quantum systems. As a consequence, quantum gravitational effects could be revealed by experiments able to test deviations from standard quantum mechanics. We have exploited the sub-millikelvin cooling of the normal modes of the ton-scale gravitational wave detector AURIGA, to place an upper limit for possible Planck-scale modifications on the ground-state energy of an oscillator, namely, the first longitudinal mode of the bar. The motion of this mode, which is symmetrical with respect to the plane perpendicular to the bar axis, implies an oscillation of the centre-of-mass of each half-bar, with a root- mean-square displacement which can be directly evaluated by the measured modal energy. We discuss some possible interpretations of our results, including possible consequences on deformed commutators, and upper limit on the length scale at which quantum fluctuations of the space-time geometry should come into play.

Relative locality in curved spacetime

Kowalski-Glikman J

In my talk I will describe kinematics and dynamics of particles with curved momentum space moving in an arbitrary curved space-time and I will argue that it may arise in a particular limit of quantum gravity. It turns out that in such theories absolute locality is replaced by a milder ‘relative locality principle.’ I will briefly discuss examples that might be of interest from the perspective of quantum gravity phenomenology program.

250 Causal loop in the theory of relative locality

Chen L

We find that Relative Locality, a recently proposed Planck-scale deformation of Special Relativity, suffers from the existence of causal loops. A simple and general construction of such on-shell loop processes is studied. We then show that even in one of the weakest deformations of the Poincar ´egroup in Relative Locality, causality can be violated.

Snyder momentum space in relative locality

Banburski A

We study the first example of a momentum space in Relative Locality with a metric connection and curvature - the de Sitter space. We show that the spacetime that emerges from Relative Locality dynamics is the classical remnant of the first ever proposed quantized spacetime - Snyder spacetime. We finish with analyzing processes described by closed loops in phase space and come to the conclusion that in a theory with curved momentum space, no more than two clocks can be synchronized simultaneously.

Sakharov’s mechanism in superfluid helium-3

Carballo-Rubio R, Barcel´oC, Garay L, Jannes G

The low-temperature phases of liquid Helium-3 are probably the complex many-body systems of which there is a better theoretical understanding, beside a great experimental control. Apart from other interesting phenomena, this system shares with other condensed matter setups the fact that some of its kinematic properties can be described within certain regimes by relativistic effective theories. Concerning this relativistic description there is another interesting point: it seems that the mechanism of dynamic induction proposed by Sakharov is not only reasonable, but in fact it could be the natural way in which the low-energy observers determine the dynamical behaviour of the effective electromagnetic and gravitational fields without knowing the high-energy physics which rule their condensed matter world. So one could consider this kind of systems (group in which we could also place theoretical deformations of superfluid Helium-3 which are not necessarily realized in Nature as condensed matter systems) as an example of a physical construction in which the idea of Sakharov is naturally included. We will discuss this possibility in detail, trying to clarify the advantages and difficulties of this approach.

New features of hawking radiation with ultraviolet dispersion

Coutant A

In 74, Hawking derived one of the main predictions of quantum field theory in classical grav- itational backgrounds. He showed that black holes should emit a steady and thermal flux of particles. In 81, Unruh proposed to mimic the behavior of fields around black hole geometries by looking at perturbations waves on a moving fluid. In particular, a fluid whose velocity crosses the speed of sound behaves much like a horizon, where the Hawking effect can be studied. In this talk, we first present the general ideas of analog models. To study the Hakwing effect, because of the infinite redshift on the horizon, one must take into account the necessary violations of Lorentz invariance at short wavelength. Using a WKB approximation, we establish under which conditions the Hawking process is recovered. We then study a

251 peculiar effect arising in some analog flows, namely white hole flows. We show that in this background, the large amplification of low frequencies through the Hawking effect leads to the emission of a large, classical wave of zero frequency but finite wavelength. We present the properties of this wave, and its birth, when it is triggered by quantum or thermal fluctuations. We also discuss the modifications introduced when the field excitations are massive.

Potential observational effects from a semiclassical approximation to quantum gravity

Bini D, Esposito G, Kiefer C, Kraemer M , Pessina F

In any approach to quantum gravity, it is crucial to look for observational effects in order to discriminate between different candidate theories. Here, we discuss how quantum-gravitational contributions to the anisotropy spectrum of the cosmic microwave background radiation arise in the framework of canonical quantum gravity by performing a semiclassical approximation to the Wheeler-DeWitt equation. This leads to a modification of the power spectrum at large scales. While the effect is currently too weak to be observable, we find an upper bound on the energy scale of inflation. We also compare these results with predictions from loop quantum cosmology.

Looking for a signature of quantum gravity in the gravitational collapse of an astrophysical object

Bambi C

In this talk, I consider a simple model describing the gravitational collapse of a star. Depending on the specific initial conditions, the outcome may be either a black hole or a naked singularity. I compute the curve luminosity of some kind of radiation (e.g. neutrinos) during the collapse, as seen by a distant observer. The curve luminosity is different is the final product is a black hole or a naked singularity. Future detections of neutrinos from supernovae may test the two scenarios. If the singularity produced in the collapse is naked, at least for a finite time, there may be a chance of observing some quantum gravity feature.

One-loop contributions in metric and pure connection formulations of gr

Groh K

A formulation of GR can be given in purely connection degrees of freedom, which is classically equivalent to Einstein’s metric description. We compute the one-loop contribution to the effective action on an instanton background and compare the result with the well-known metric case. Here we observe that the difference is exactly given by the scalar modes present in the latter. Furthermore, there is some evidence to expect that the difference is always given by an integer, suggesting a profound connection between both theories even at the quantum level.

252 Non-gaussian stochastic gravity

Bates J

Stochastic gravity is a theoretical framework in which the backreaction problem of semiclassical gravity is treated as a quantum open system, with quantum matter fields playing the role of the environment and the metric field that of the system of interest. This paradigm allows us to account for the effects of quantum fluctuations of the matter fields via a Langevin-like semiclassical equation for the metric perturbations induced by the fluctuations. In this talk, I will present a reformulation of stochastic gravity which incorporates the higher moments of the fluctuations of the quantum stress tensor operator to generate non-Gaussian behavior. In addition, I will demonstrate a scheme for computing realizations of these non-Gaussian fluctuations and the resulting probability distribution of the stress tensor fluctuations, and discuss the implications this non-Gaussian behavior may have upon the geometry of spacetime at short distance scales.

253 Poster session

Warped ads3 black holes in 3d gravity: instabilities and quantum effects

Ferreira H

3D gravity allows us to study aspects of General Relativity and quantum gravity in a simpler technical setting which retains much of the conceptual complexity of the 4D version. However, pure Einstein gravity has no local degrees of freedom in 3D. Topologically Massive Gravity is a deformation of pure Einstein gravity which adds a gravitational Chern-Simons term and includes propagating gravitons. For many years several attempts at finding a stable vacuum solution for this theory were made and it has been recently established that the Anti-de Sitter (AdS3) solution is unstable for almost all values of the coupling constant of the Chern-Simons term. Warped AdS3 solutions are recent candidates for a stable vacuum solution. In this talk I first describe these solutions and the black hole spacetimes obtained from them. In addition, I consider scalar field perturbations on these black hole backgrounds and discuss the issue of classical stability to these perturbations and progress towards determining the renormalized stress energy tensor for the Hartle-Hawking vacuum state.

Detector for a massless (1+1) field: hawking effect without infrared sickness

Juarez Aubry B

We modify the Unruh-DeWitt particle detector by coupling the detector’s monopole moment to the derivative of a (1+1)-dimensional scalar field, rather than the field itself. We show that issues of time- dependency in the trajectory, the quantum state and the switching can be handled within first-order perturbation theory essentially as for a non-derivative coupling in 3+1 dimensions. Crucially, we present evidence that the detector remains well-behaved in the limit of a massless field, despite the divergence in the two-point function, and we use the detector to analyse the onset of the Hawking and Unruh effects in strongly time-dependent situations.

Dependence of thermal averages for a scalar field on the curvature coupling parameter

De Lorenci V, Gomes L, Moreira E

It is fairly well known that when spacetime is flat the curvature coupling parameter does not appear in the equation of motion of a massless scalar field (wave equation); but it does appear in the corresponding stress-energy-momentum tensor. The reason for such is that the variation of the action with respect to the metric that leads to the expression for the stress-energy-momentum tensor is made before solving the Einstein equations which yield the flat geometry. In this work a massless quantum scalar field at finite temperature is studied in the half space (Minkowski spacetime with a single flat wall dividing space in two half spaces) with arbitrary number of dimensions, assuming the Dirichlet boundary condition on the wall. We show that local thermal averages, such as the energy density, depend on the curvature coupling parameter. Their behaviors near the wall and deep in the bulk are confronted, revealing interesting features which would be missed if the standard procedure to address radiation in statistical mechanics had otherwise been applied. In particular we show that “Stefan’s constant” depends on the curvature coupling parameter and that not all values of the latter are physically acceptable.

254 Semiclassical analysis of the scalar geodesic synchrotron radiation in kerr spacetime

Crispino L, Macedo C, Cardoso V

We analyze the scalar synchrotron radiation emitted by a source in circular orbits, stable and unstable, direct and retrograde, around a rotating black hole within the framework of quantum field theory in curved spacetimes at tree level. We also analyze the radiation which escapes to infinity, showing that, in accordance with superradiance, it can be amplified for the case of direct orbits.

States of low energy and “modified sorkin-johnston states” on minkowski and expanding spacetimes

Oliveira M

We show how to construct Hadamard states on the algebra of the Klein-Gordon field on both static and expanding, homogeneous and inhomogeneous spacetimes with compact Cauchy surfaces. These constructions will be performed in two different ways. First, we construct states that minimize the expectation value of the renormalized energy density, smeared with compactly supported test functions over a timelike subregion of spacetime. Second, we consider the recent definition of Sorkin-Johnston states given by Afshordi et al. (2012) which were shown not to be Hadamard states (Fewster and Verch, 2012). We present a modification of this definition and prove that we obtain Hadamard states.

Vacuum awakening effect in spheroidal and rotating configurations, and its relation to the classical instability

Mendes R

Recently, it has been shown how the quantum fluctuations of a free scalar field properly coupled to the curvature can drive an instability of the spacetime configuration. This mechanism might have observable astrophysical implications, for instance, in the formation of compact stars. Also, the observation of relativistic stars with certain mass-radius ratios could in principle be used to discard an entire range of field-to-scalar-curvature couplings as physically reasonable. For this latter purpose, it is relevant to know if the main features described in the original works are preserved when assumptions such as spherical symmetry or staticity are relaxed. In this presentation, we discuss this mechanism in the context of (spheroidal and rotating) thin shells, exploring the consequences of deviations from spherical symmetry and staticity on the triggering of the effect. We also make explicit the relation between this vacuum awakening effect and the related classical instability.

Fermions on ads

Ambrus V

We construct and renormalise the vacuum Feynman propagator for Dirac fermions on anti-de Sitter space-time, from which we calculate renormalised vacuum and finite temperature expectation values. We then consider vacuum and thermal states rotating with a constant angular velocity, whose properties we compare to those for rotating states in Minkowski space-time.

255 Various aspects of radiative thermality in ds spacetime

Singh S, Ganguly C, Padmanabhan T

We look at the quantization and particle creation aspects of massless scalar field in time-dependent form of the flat de Sitter spacetime. The question of massless scalar particle creation is dealt with from two viewpoints. We first observe the radiation emission by calculating the power spectrum of the evolved field state initially prepared as a positive frequency mode. From a second angle, we study the particle creation from the viewpoint of a detector coupled with the field in the dS geometry. For completeness and as a validity check we also show that the vacuum state defined with respect to the time-dependent dS coordinates does appear thermal if veiwed in the static patch. Finally we consider the effects of a small perturbation to the de Sitter metric in a quasi de Sitter scenario on the power spectrum of the field modes. We demonstrate a specific example using the late time accelerated phase of the universe.

S-matrix for anti de sitter spacetimes through general boundary qft

Dohse M , Oeckl R

We present recent results in the construction of an S-MATRIX for real Klein-Gordon fields on ANTI DE SITTER (AdS) spacetimes. As well known, the standard construction of an S-matrix fails here, since no asymptotically free states exist on AdS. The GENERAL BOUNDARY FORMULATION (GBF) of Quantum Theory provides a way to construct a new S-matrix, using quantum states on timelike hypercylinder surfaces. The GBF is a framework for Quantum Theory that aims at (re)constructing it in a more covariant way than the standard formulation. To this end, it lets states live on the boundaries of spacetime regions (instead of the usual Cauchy surfaces). From this premise, generalized transition amplitudes, observables and a probability interpretation have been developed. A key property is that in the standard situation (states on equal-time surfaces) the GBF nicely reproduces the results of the standard formulation of Quantum Theory. Thus the GBF is a framework for QFT on curved spacetimes. However, since it does not need a fixed background metric in the spacetime regions, it also provides new possibilities for approaching Quantum Gravity. We begin the talk with a concise presentation of the GBF. Then we sketch the construction of our S- matrix in the Holomorphic Quantization, and comment on the corresponding Schr¨odingerRepresentation. Finally, we look at the properties of this S-matrix, for example, how we implement its invariance under actions of AdS’s isometry group SO(2,3).

Tunneling transitions with gravity in flat potentials

Lavrelashvili G

We consider tunneling transitions in scalar field theory minimally coupled to gravity and investigate case of relatively flat potentials. In particular we study in detail properties of Fubini instantons and their generalizations. First we show that Fubini instantons in flat spacetime possess single negative mode in spectrum of small perturbations, i.e. they are in fact bounces and describe decay processes. Then we review what is known for generalization of Fubini instantons on maximally symmetric backgrounds. In case of self consistent solutions with gravity we analyze situations with different values of cosmological constant separately. We also investigate spectrum of linear perturbations about these solutions, and present solutions which have exactly one negative mode and describe tunneling and also other branches of solution which have extra instabilities.

256 Spin 3/2 fields in higher-dimensional spherically symmetric black hole spacetime

Chen C

Using the iterative method of Camporesi and Higuchi, we obtain the eigenvalues, the eigenfunctions and the corresponding degeneracies of spinor-vectors on N-spheres. With these results we shall derive the radial equation of a spin-3/2 field in a spherically symmetric black hole spacetime. The radial equation can be solved using the WKB or other semianalytic methods. Then we can discuss the interesting problems of quasinormal modes and the Hawking radiations in these situations.

Absorption and scattering of sound waves in draining bathtub via complex angular momentum method

Oliveira L, Dolan S, Crispino L

In 1981, W. G. Unruh showed that under certain conditions, sound waves in a fluid may be governed by a Klein-Gordon equation on an “effective spacetime” determined by the background flow properties. Here we consider the spacetime of the draining bathtub: a circulating, draining flow whose effective spacetime shares key features with the rotating black hole (Kerr) spacetime. We present a complete investigation of the role of Regge pole resonances of this system. We then explore the geometric link between (prograde and retrograde) null geodesic orbits on the spacetime, and the properties of the Regge pole spectra. We apply a “geodesic-expansion” method which leads to asymptotic expressions for the spectra, the radial functions, and the residues. Next, the role of the Regge poles in scattering and absorption processes is studied through the application of the complex angular momentum method. We elucidate the link between the Regge poles and oscillations in the absorption cross section. Finally, we show that Regge poles provide a neat explanation for “orbiting” oscillations seen in the scattering cross section.

A new perspective on path integral quantum mechanics in curved space-time

Singh D, Mobed N

A new approach to path integral quantum mechanics in curved space-time for a scalar particle is presented in terms of local curvature involving Fermi or Riemann normal co-ordinates. This approach involves use of a local time translation operator with Lie transport that, while strictly non-unitary in form, nonetheless yields the correct expression for the curved space-time free-particle Lagrangian in the sum- over-histories, with additional terms corresponding to a curvature-dependent violation of probability. These terms simultaneously induce a breakdown of time-reversal symmetry at the quantum mechanical level, and also a violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the scalar propagator generates a gravitational analogue of the Aharonov-Bohm effect and Berry’s phase through the appearance of an overall gauge-invariant phase factor. Future directions to follow from this initial research are presented.

Scalar contribution to the graviton self-energy during inflation

Park S, Woodard R

Primordial inflation results in the production of a vast ensemble of highly infrared, massless, minimally coupled scalars. We use dimensional regularization to evaluate the one loop contribution to the graviton

257 self-energy from these scalars on a locally de Sitter background. We absorb the ultraviolet divergences using the R2 and C2 counterterms first derived by ’t Hooft and Veltman, and we take the D = 4 limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. This fully renormalized form can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity. We have seen that they have no effect on the propagation of dynamical gravitons. Our computation motivates a conjecture for the first correction to the vacuum state wave functional of gravitons. We comment as well on performing the same analysis for the more interesting contribution from inflationary gravitons, and on inferring one loop corrections to the force of gravity.

Quantum gravitational effects on massive fermions dirung inflation

Miao S

We compute the one loop graviton contribution to the self-energy of a very light fermion on a locally de Sitter background. This result can be used to study the effect that a small mass has on the propagation of fermions through the sea of infrared gravitons generated by inflation. We employ dimensional regu- larization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for two noninvariant counterterms owing to the breaking of de Sitter invariance by our gauge condition.

An invariant measure of spacetime expansion for lambda-driven inflation

Woodard R, Tsamis N

It is difficult to evaluate claims about the quantum field theoretic back-reaction on inflation without possessing a reliable technique for quantifying the expansion rate. There is a standard technique in sclar-driven inflation but not yet for pure quantum gravity. I explain the problem, propose a suitable observable, and present results from a one loop computation of it.

Graviton corrections to the vacuum polarization

Leonard K , Woodard R

This work focuses on one-loop corrections to the vacuum polarization from gravitons in flat space and de Sitter space. In the flat space regime we use the result for the BPHZ renormalized vacuum polarization to quantum correct Maxwell’s equations and consider several sources. These sources include dynamical photons, an alternating point dipole, a point source, and the instantaneous dipole which gives rise to the fascinating ”smearing of the light-cone’” effect. This work serves as an example for calculating the vacuum polarization in de Sitter space, which is important for studying primordial inflation. In de Sitter we again find the renormalized vacuum polarization, use it to quantum correct Maxwelll’s equations and consider the effects this has on dynamical photons.

Covariant phase space symplectic form and peierls inversion formula in the presence of constraints and gauge

Khavkine I

It is well known that a Poisson bracket may be constructed for a field theory directly from its Lagrangian

258 using the Peierls formula. However the Peierls formula requires the existence of some retarded and advance Green functions, which is not automatic. It is also well known that the canonical symplectic form may also be be constructed directly from the Lagrangian using the covariant phase space method. An elegant argument showing that these two formulas are mutually inverse in the case of scalar field theory with normally hyperbolic equations of motion was given by Forger & Romero [arXiv:math-ph/0408008]. I generalize their argument to arbitrary field theories, which may have constraints and be gauge invariant, provided certain sufficient conditions hold. These conditions include symmetric hyperbolizability of the equations of motion and the vanishing of certain cohomologies of elliptic complexes that extend the constraints and the gauge generators. Based on p art of [arXiv:1211.1914].

Propagator of a scalar field on a stationary slowly varying gravitational background

Kazinski P

The propagator of a scalar field on a stationary slowly varying in space gravitational background is derived retaining only the second derivatives of the metric. The corresponding one-loop effective action is constructed. The propagator and the effective action turn out to depend nontrivially on the Killing vector defining the vacuum state and the Hamiltonian of a scalar field. The Hawking particle production is described in the quasiclassical approximation and the quasiclassical formula for the Hawking temper- ature is derived. The behaviour of the Unruh detector on a curved background is considered and the quasiclassical formula for the Unruh acceleration determining the Unruh temperature is derived. The ra- diation reaction problem on a curved background is discussed in view of the new approximate expression for the propagator. The correction to the mass squared of a scalar particle on a stationary gravitational background is obtained. This correction is analogous to the quantum correction to the particle mass in a strong electromagnetic field. For a vacuum solution to the Einstein equations, it is equal to minus one-fourth of the free fall acceleration squared.

Deformed lorentz symmetry in expanding spacetimes and gamma-ray-bursts

Rosati G

Observations of bursts of particles from cosmological distances are being used to test for a momentum dependence of the speed of photons, partly motivated by preliminary results reported in analyses of some quantum-spacetime scenarios. The relationship between time of arrival, momentum of the photon and redshift of the source which is used for these purposes assumes a ”breakdown” of relativistic symmetries, meaning that it is a preferred-frame scenario which does not satisfy the Relativity Principle. The alter- native hypothesis of a ”deformation” of relativistic symmetries, which preserves the Relativity Principle by adopting deformed laws of relativistic transformation between observers, could not so far be tested in gamma-ray-burst observations because it was not known how to formulate it in expanding spacetimes. Starting from our recent results Phys.Rev.D86(2012)124035, we here provide such a formulation, and we find that also for the symmetry-deformation scenario the analysis of gamma-ray-burst data take us very close to the desired ”Planck-scale sensitivity”.

Quantum-to-classical transition and gravity-induced instabilities (in progress)

Couto Correa de Lima W

It was recently shown that gravitational fields produced by realistic matter distributions can induce the vacuum fluctuations of some non-minimally coupled free scalar field to go through a phase of exponential

259 amplification. For the particular case of the formation of a neutron star, the vacuum energy density of the field rivals the one of the star in a lapse of just a few milliseconds, from which backreaction effects must be considered. Classical analyses have revealed that, at least for some values of the mass-radius ratio of the star and the non-minimal coupling parameter, a non-null scalar field profile could stabilize the system. The aim of our study is to shed some light on the backreaction process in the context of the quantum-to-classical transition that will occur once the classical background spacetime reacts to the unstable quantum field.

Quantum fluctuations of a time delay observable in the Minkowski vacuum linearized gravity

Bonga B, Khavkine I

I will discuss a clock synchronization thought experiment modeled by a diffeomorphism invariant ”time delay” observable. In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime. Thus, upon quantization, it is sensitive to the long expected smearing of the light cone by vacuum fluctuations in quantum gravity. After perturbative linearization, its mean and variance are computed in the Minkowski Fock vacuum of linearized gravity. The naive divergence of the variance is meaningfully regularized by a length scale µ, the physical detector resolution. This is the first time vacuum fluctuations have been fully taken into account in a similar calculation. Despite some drawbacks this calculation provides a useful template for the study of a large class of similar observables in quantum gravity. Due to their large volume, intermediate calculations were performed using computer algebra 2 software. The resulting variance scales like (s`p/µ) , where `p is the Planck length and s is the distance scale separating the (”lab” and ”probe”) clocks. Additionally, the variance depends on the relative velocity of the lab and the probe, diverging for low velocities. This puzzling behavior may be due to an oversimplified detector resolution model or a neglected second order term in the time delay.

Particle creation due to tachyonic instability in relativistic stars

Landulfo A, Lima W, Matsas G, Vanzella D

Dense enough compact objects were recently shown to lead to an exponentially fast increase of the vacuum energy density for some free scalar fields properly coupled to the spacetime curvature as a consequence of a tachyonic-like instability. Once the effect is triggered, the star energy density would be overwhelmed by the vacuum energy density in a few milliseconds. This demands that eventually geometry and field evolve to a new configuration to bring the vacuum back to a stationary regime. Here, we show that the vacuum fluctuations built up during the unstable epoch lead to particle creation in the final stationary state when the tachyonic instability ceases. The amount of created particles depends mostly on the duration of the unstable epoch and final stationary configuration, which are open issues at this point. We emphasize that the particle creation coming from the tachyonic instability will occur even in the adiabatic limit, where the spacetime geometry changes arbitrarily slowly, and therefore is quite distinct from the usual particle creation due to the change in the background geometry.

New fundamental wave equation on curved space-time and its inflationary applications

Musielak Z , Fry J

A method of identifying elementary waves on curved space-time manifolds of General Relativity and the principle of relativity are used to derive two sets of fundamental higher derivative wave equations. One

260 of these sets contains the original curved space-time Klein-Gordon equation, and it is shown that all physically-acceptable solutions to the higher derivative wave equations in this set are the same as the solutions to the Klein-Gordon equation, which means that the equation is the only fundamental wave equation available to construct (local) quantum field theories on curved space-time manifolds. However, for the other set, it is demonstrated that all physically-acceptable solutions to the higher derivative wave equations are the same as the solutions to the lowest order fundamental wave equation in this set. As a result, this lowest order wave equation is the only new fundamental equation in the set, and it can be used to construct higher derivative (non-local) quantum field theories on curved space-time manifolds. A scalar field described by this new fundamental wave equation is considered as an inflation field, and its applications to the early stages of the Universe as well as to Dark Energy are discussed.

Beyond fock space in 3d gravity

Arzano M, Kowalski-Glikman J, Trze´sniewskiT

A (relativistic) point particle in 2+1-dimensional gravity is known to possess the momentum manifold which is a Lie group. Quantization of a system of such particles is given in terms of a deformation of the group of usual relativistic symmetries. Quantum fields carry representations of these symmetries. Without delving to much in the mathematical structures, I will discuss how the non-trivial geometry of the momentum space leads to the deformed algebra of creation and annihilation operators. In particular, a connection with the so-called braided field theory will be described. In this way the Fock space can be consistently constructed, which also reduces to that of the ordinary quantum field theory when gravitational constant vanishes. It also sheds some light on the 4-dimensional case.

Non-planar loops and total momentum non-conservation in relative locality

Banburski A

Recent work in Relative Locality has shown that the theory allows for a solution of an on-shell causal loop. We show that the theory contains a different type of a loop in which locally momenta are conserved, but there is no global momentum conservation. Thus a freely propagating particle can decay into two particles, which later recombine to give a particle with momentum and mass different than the original one.

Absorption and Scattering of Sound Waves in a Draining Bathtub

Crispino L

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