iopscience.org/cqg Classical and Quantum Gravity Highlights of 2008/2009 Cover image: Colour-coded TM reflectivity of a waveguide structure versus groove depth and waveguide thickness A Bunkowski et al 2006 Class. Quantum Grav. 23 7297–303. Classical and Quantum Gravity

Dear Colleague, There has never been a better time to publish in Classical and Quantum Gravity (CQG). In 2009, CQG was awarded its highest ever impact factor of 3.035 and the journal continues to publish more and more exciting research from all areas of gravitational physics. As always, CQG offers the most rigorous peer review in the field with all papers being carefully appraised by 2 independent reviewers. 2010 is sure to be more exciting still. One of the most important recent developments has been the commissioning of special ‘Cluster’ issues, which are small, focussed, invitation-only issues of the journal targeting the best research in topical areas of gravitational physics. In 2010, CQG will present a cluster issue on Nonlinear Cosmological Perturbation Theory and a double-issue of selected Numerical Relativity and Relativistic Astrophysics content presented at the Impact Factor NRDA 2009 and MICRA 2009 meetings. 3.035* In this brochure, you may browse the abstracts of a selection of articles chosen * As listed in ISI®’s 2008 Science by CQG’s Editorial Board in June 2009 as the CQG Highlights of the previous Citation Index Journal citation reports 12 months. Each article can be found online at iopscience.org/cqg and will be free to Readership by regions in 2009 download until 1 November 2010. Europe 28% ROW 26% I’d like to take this opportunity to thank all of the authors and referees who give their support to CQG. I hope that you will consider CQG your first choice venue for publication of your next paper!

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Editor-in-Chief Full-text downloads Clifford M Will 200 000

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Image taken from: ‘Titania-doped tantala/silica Images taken from: ‘A detailed analytic study of the Image taken from: ‘Simulating the emission and coatings for gravitational-wave detection’ asymptotic quasinormal modes of Schwarzschild– outflows from accretion disks’ S C Noble et al G M Harry et al 2007 Class. Quantum Grav. anti de Sitter black holes’ R G Daghigh and M D 2007 Class. Quantum Grav. 24 S259–S274. 24 405–15. Green 2009 Class. Quantum Grav. 26 125017.

Highlights 2009 3 Classical and Quantum Gravity

Contents

page Topical Reviews 8 Fast Track Communications 8 Special issue articles 10 Regular papers 12 •Cosmology 12 •Experimental Gravity 14 •Mathematical General Relativity 15 •Numerical Relativity 16 •Black Holes 16 •Quantum Cosmology 17 •Quantum Gravity 19 •Strings, Branes, Supergravity, Gauge Theory 20 •Geometry, Topology 21 •Comments, Replies and Notes 22

Journal Scope

Published twice monthly (24 issues per year), Classical and Quantum Gravity publishes original research articles on the subjects of gravitational physics and the theory of spacetime. The readership comprises gravitational theorists and experimentalists in physics, mathematics and cosmology.

Papers are published under the following areas: •Classical general relativity •Applications of relativity •Experimental gravitation •Cosmology and the early universe •Quantum gravity •Supergravity, superstrings and supersymmetry •Mathematical physics relevant to gravitation

More information on each of these areas can be found at iop.org/cqg.

Images taken from: ‘Quasinormal modes of black holes and black branes’ E Berti et al 2009 Class. Quantum Grav. 26 163001.

4 Highlights 2009 Classical and Quantum Gravity

Editorial Board

Editor-in-Chief C M Will, Washington University, St Louis, USA

Editorial Board L Andersson, University of Miami, USA B Mours, Laboratoire d’Annecy-le-Vieux de Physique des Particules, France V Balasubramanian, University of Pennsylvania, Philadelphia, USA S Mukohyama, IPMU, University of Tokyo, Japan A A Coley, Dalhousie university, Halifax, Canada N Ó Murchadha, University College Cork, Ireland A Corichi, Universidad Nacional Autónoma de México (UNAM), E Poisson (Book Reviews Editor), University of Guelph, Guelph, Canada Morelia, Mexico L Rezzolla, Max-Planck-Institut für Gravitationsphysik, Golm, Germany S Dhurandhar, Inter-University Centre for Astronomy and Astrophysics, V O Rivelles, Universidade de Sao Paulo (USP), Sao Paulo, Brazil Pune, India S F Ross, Durham University, Durham, UK V P Frolov, University of Alberta, Edmonton, Canada C Rovelli, Université de la Mediterranée–Aix-Marseille II, France D Garfinkle, Oakland University, Rochester, MI, USA J Samuel, Raman Research Institute, India G Gonzalez, Louisiana State University, Baton Rouge, USA M Sasaki, Kyoto University, Japan J Isenberg, University of Oregon, Eugene, USA J M M Senovilla, Universidad del País Vasco, Bilbao, Spain K Kuroda, University of Tokyo, Japan C C Speake, University of Birmingham, Birmingham, UK L Lehner, Louisiana State University, Baton Rouge, USA D Sudarsky, Universidad Nacional Autónoma de México (UNAM), R B Mann, University of Waterloo, Ontario, Canada Morelia, Mexico M Mars, Universidad de Salamanca, Spain R-S Tung, Shanghai Normal University, Shanghai, China P R L V Moniz, Universidade da Beira Interior, Covilhã, Portugal D Wands, University of Portsmouth, UK

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Top 20 Most Downloaded articles from Vol 26 (2009)

1 What is a particle? Daniele Colosi et al 2009 Class. Quantum Grav. 26 025002 (22pp)

2 Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project Benjamin Aylott et al 2009 Class. Quantum Grav. 26 165008 (51pp)

3 Local Hawking temperature for dynamical black holes S A Hayward et al 2009 Class. Quantum Grav. 26 062001 (8pp)

4 The double pulsar system: a unique laboratory for gravity M Kramer et al 2009 Class. Quantum Grav. 26 073001 (20pp)

5 The gravitational-wave signature of core-collapse supernovae Christian D Ott 2009 Class. Quantum Grav. 26 063001 (48pp)

6 The information paradox: a pedagogical introduction Samir D Mathur 2009 Class. Quantum Grav. 26 224001 (31pp)

7 The alternative to classical mass renormalization for tube-based self-force calculations Andrew H Norton 2009 Class. Quantum Grav. 26 105009 (19pp)

8 LISA Pathfinder: the experiment and the route to LISA M Armano et al 2009 Class. Quantum Grav. 26 094001 (18pp)

9 Quasinormal modes of black holes and black branes Emanuele Berti et al 2009 Class. Quantum Grav. 26 163001 (108pp)

10 Warped AdS3 black holes in new massive gravity Gérard Clément 2009 Class. Quantum Grav. 26 105015 (11pp)

11 Hamiltonian general relativity and the Belinskii–Khalatnikov–Lifshitz conjecture Abhay Ashtekar et al 2009 Class. Quantum Grav. 26 052001 (10pp)

12 The path to the enhanced and advanced LIGO gravitational-wave detectors J R Smith et al 2009 Class. Quantum Grav. 26 114013 (8pp)

13 On the resolution of the big bang singularity in isotropic loop quantum cosmology Madhavan Varadarajan 2009 Class. Quantum Grav. 26 085006 (21pp)

14 Lectures on holographic methods for condensed matter physics Sean A Hartnoll 2009 Class. Quantum Grav. 26 224002 (61pp)

15 The tensor-vector-scalar theory and its cosmology Constantinos Skordis 2009 Class. Quantum Grav. 26 143001 (43pp)

16 What is the entropy of the universe? Paul H Frampton et al 2009 Class. Quantum Grav. 26 145005 (7pp)

17 Gravity and hydrodynamics: lectures on the fluid-gravity correspondence Mukund Rangamani 2009 Class. Quantum Grav. 26 224003 (48pp)

18 Status of NINJA: the Numerical INJection Analysis project Laura Cadonati et al 2009 Class. Quantum Grav. 26 114008 (13pp)

19 A new proof of the Bianchi type IX attractor theorem J Mark Heinzle et al 2009 Class. Quantum Grav. 26 075015 (28pp)

20 Geodesics and symmetries of doubly spinning black rings Mark Durkee 2009 Class. Quantum Grav. 26 085016 (33pp)

Highlights 2009 7 Classical and Quantum Gravity

Highlighted Topical Reviews The double pulsar system: a unique CQG publishes Topical Reviews in various areas of laboratory for gravity gravitational physics. The Reviews are carefully chosen and M Kramer and N Wex invited to the journal by the Editorial Board. They provide 1 timely and authoritative information in areas where there has 2009 Class. Quantum Grav. 26 073001 been significant recent progress. The Topical Reviews are among the most downloaded articles in CQG. The PSR J0737–3039 is a double neutron star system in which both stars are detectable as active radio pulsars. The pair, consisting of an old, mildly recycled 23-ms pulsar and a young 2.8-s pulsar, orbit the common centre A concise introduction to perturbation of mass in a slightly eccentric, compact orbit with a short orbital period of theory in cosmology 147 min. The combination of system parameters makes this binary pulsar the most relativistic binary pulsar known and allows unique tests of general Karim A Malik and David R Matravers relativity and alternative theories of gravity. Hence, we summarize the importance of the system for such tests, and pay attention, for instance, to 2008 Class. Quantum Grav. 25 193001 the observed measurement of relativistic spin precession which confirms the ‘effacement’ property of a spinning body. We also present a method to use measurements of the absolute position angle of the linearly polarized We give a concise, self-contained introduction to perturbation theory radio emission of the pulsars to measure the rate of the relativistic spin in cosmology at linear and second orders, striking a balance between precession. We demonstrate how spin–orbit coupling will eventually allow mathematical rigour and usability. In particular, we discuss gauge us to determine the moment-of-inertia of pulsar A, and provide a general issues and the active and passive approaches to calculating gauge outlook into the prospects of future observations of the double pulsar. transformations. We also construct gauge-invariant variables, including the second-order tensor perturbation on uniform curvature hypersurfaces.

The gravitational-wave signature of Median receipt to first decision times core-collapse supernovae Regular papers FTCs Christian D Ott 49 DAYS 30 DAYS 2009 Class. Quantum Grav. 26 063001 Highlighted Fast Track We present an extensive review of the ensemble of anticipated Communications gravitational-wave (GW) emission processes in stellar core collapse and postbounce core-collapse supernova evolution. Galactic core-collapse The exclusive Fast Track Communications section welcomes supernovae are very rare events, but within 3 5 Mpc from Earth, the rate 2 short, high impact submissions of strictly 8 pages or less. FTCs are among the most downloaded articles in CQG. jumps to 1 in ~2 years. Using the set of currently available theoretical gravitational waveforms, we compute upper-limit optimal signal-to-noise FTCs are free to read for 10 years following publication. ratios based on current and advanced LIGO/GEO600/VIRGO noise curves Fast T r ack Communications for the recent SN 2008bk which exploded at ~3.9 Mpc. While initial LIGOs cannot detect GWs emitted by core-collapse events at such a distance, we find that advanced LIGO-class detectors could put significant upper limits on the GW emission strength for such events. We study the potential Multiple M2-branes and the embedding occurrence of the various GW emission processes in particular supernova explosion scenarios and argue that the GW signatures of neutrino-driven, tensor magneto-rotational, and acoustically-driven core-collapse SNe may be Eric A Bergshoeff, Mees de Roo and Olaf Hohm mutually exclusive. We suggest that even initial LIGOs could distinguish these explosion mechanisms based on the detection (or non-detection) of 2008 Class. Quantum Grav. 25 142001 GWs from a galactic core-collapse supernova. Figure 4. Colormap depicting the specific entropy distribution in the equatorial plane of We show that the Bagger–Lambert theory of multiple M2-branes fits into the 20-M_ model s20A2B4 of Ott et al [42, 119, the general construction of maximally supersymmetric gauge theories 115] at 90 ms after core bounce. Red and yellow using the embedding tensor technique. We apply the embedding tensor regions of the PNS core have lowentropy (*1–3 kB baryon*1) while dark blue and black symbol- technique in order to systematically obtain the consistent gaugings of N = 8 ize high entropy >6 kB baryon*1. The nonaxisym- superconformal theories in 2 + 1 dimensions. This leads to the Bagger– metric structures are of primarily m = {1, 2, 3} Lambert theory, with the embedding tensor playing the role of the four-index nature with radial variations in dominance. antisymmetric tensor defining a ‘3-algebra’. We present an alternative formulation of the theory in which the embedding tensor is replaced by a set of unrestricted scalar fields. By taking these scalar fields to be parity-odd, the Chern–Simons term can be made parity-invariant.

8 Highlights 2009 Classical and Quantum Gravity

A simple proof of the recent generalizations Ricci flows, wormholes and critical of Hawking’s black hole topology theorem phenomena István Rácz Viqar Husain and Sanjeev S Seahra

2008 Class. Quantum Grav. 25 162001 2008 Class. Quantum Grav. 25 222002

A key result in four-dimensional black hole physics, since the early 1970s, We study the evolution of wormhole geometries under the Ricci flow using is Hawking’s topology theorem assertion that the cross-sections of an numerical methods. Depending on values of initial data parameters, ‘apparent horizon’, separating the black hole region from the rest of the wormhole throats either pinch off or evolve to a monotonically growing spacetime, are topologically 2-spheres. Later, during the 1990s, by state. The transition between these two behaviors exhibits a form of critical applying a variant of Hawking’s argument, Gibbons and Woolgar could phenomena reminiscent of that observed in gravitational collapse. Similar also show the existence of a genus-dependent lower bound for the entropy results are obtained for initial data that describe space bubbles attached of topological black holes with negative cosmological constant. Recently, to asymptotically flat regions. Our Hawking’s black hole topology theorem, along with the results of Gibbons numerical methods are applicable to and Woolgar, has been generalized to the case of black holes in higher ‘matter-coupled’ Ricci flows derived from dimensions. Our aim here is to give conformal invariance in string theory. a simple self-contained proof of these generalizations, which also Figure 4. Embedding diagrams of 3-geometries makes their range of applicability representing a bubble connecting two transparent. asymptotically flat regions.

Figure 1. The black hole, represented by the shaded region, is bounded by horizon H that is foliated by MOTS’ homologous to . Semi-classical central charge in topologically massive gravity A universal inequality between the angular Geoffrey Compère and Stéphane Detournay momentum and horizon area for 2009 Class. Quantum Grav. 26 012001 axisymmetric and stationary black holes It is shown that the warped black hole geometries discussed recently in with surrounding matter arXiv:0807.3040 (Anninos et al 2008) admit an algebra of asymptotic Jörg Hennig, Marcus Ansorg and Carla Cederbaum symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry 2008 Class. Quantum Grav. 25 162002 by canonical charges allows us to find the central charge of the Virasoro algebra. The right-moving central charge ()53vlˆ2 + CR =− We prove that for sub-extremal axisymmetric and stationary black holes with G)vˆ(ˆv2 + 3 arbitrary surrounding matter the inequality 8π|J| < A holds, where J is the is obtained when the Virasoro generators are normalized in order to have a angular momentum and A the horizon area of the black hole. positive zero-mode spectrum for the warped black holes. If one normalizes the Virasoro generators in order to have a positive central charge, the zero mode is then unbounded from below. The current algebra is also shown to The inner Cauchy horizon of axisymmetric be centrally extended. and stationary black holes with surrounding matter Hamiltonian general relativity and the Marcus Ansorg and Jörg Hennig Belinskii–Khalatnikov–Lifshitz conjecture 2008 Class. Quantum Grav. 25 222001 Abhay Ashtekar, Adam Henderson and David Sloan 2009 Class. Quantum Grav. 26 052001 We investigate the interior of regular axisymmetric and stationary black holes surrounded by matter and find that for non-vanishing angular The Belinkskii, Khalatnikov and Lifshitz conjecture says that as one momentum of the black hole the spacetime can always be extended approaches spacelike singularities in general relativity, ‘time derivatives regularly up to and including an inner Cauchy horizon. We provide an explicit dominate over spatial derivatives’ so that the dynamics at any spatial relation for the regular metric at the inner Cauchy horizon in terms of that point is well captured by an ordinary differential equation. By now at the event horizon. As a consequence, we obtain the universal equality considerable evidence has accumulated in favor of these ideas. Starting (8πJ)2 = A+A− where J is the black hole’s angular momentum and A− and A+ with a Hamiltonian framework, we provide a formulation of this conjecture denote the horizon areas of inner Cauchy and event horizons, respectively. in terms of variables that are tailored to non-perturbative quantization. We also find that in the limit J  0 the inner Cauchy horizon becomes Our formulation serves as a first step in the analysis of the fate of generic singular. spacelike singularities in loop quantum gravity.

Highlights 2009 9 Classical and Quantum Gravity

Highlighted Special issue Articles Emergent horizons in the laboratory Ralf Schützhold CQG seeks high quality articles of a common theme for special issues. CQG special issues differ from proceedings 2008 Class. Quantum Grav. 25 114011 volumes in that all articles are peer reviewed to CQG’s 3 usual high standards. The concept of a horizon known from general relativity describes the loss of causal connection and can be applied to non-gravitational scenarios Observing dark energy such as out-of-equilibrium condensed-matter systems in the laboratory. Daniel J Eisenstein This analogy facilitates the identification and theoretical study (e.g. regarding the trans-Planckian problem) and possibly the experimental 2008 Class. Quantum Grav. 25 114001 verification of ‘exotic’ effects known from gravity and cosmology, such as Hawking radiation. Furthermore, it yields a unified description and better understanding of non-equilibrium phenomena in condensed-matter systems I review the observational evidence for dark energy, arguing that the and their universal features. By means of several examples including large-scale structure observed at low redshift and in the cosmic microwave general fluid flows, expanding Bose–Einstein condensates and dynamical background offers a strong corroboration of the supernova Ia results. quantum phase transitions, the concepts of event, particle and apparent The angular scale of the acoustic oscillations in the cosmic microwave horizons will be discussed together with the resulting quantum effects. background strongly support a nearly flat universe, while many arguments from low-redshift cosmology support a matter density around 25% of the critical density. The observational constraints on the cosmological model have improved dramatically over the past decade. The coming decade will likely bring another two to three orders of magnitude in improvements in the data sets used for the study of dark energy.

Quark soup al dente: applied superstring Figure 2. Sketch of the origin of Hawking radiation (red curves) in a de Laval nozzle. theory R C Myers and S E Vázquez

2008 Class. Quantum Grav. 25 114008 dc readout experiment at the Caltech 40m prototype interferometer R L Ward et al In recent years, experiments have discovered an exotic new state of matter known as the strongly coupled quark–gluon plasma (sQGP). At 2008 Class. Quantum Grav. 25 114030 present, it seems that standard theoretical tools, such as perturbation theory and lattice gauge theory, are poorly suited to understand this new phase. However, recent progress in superstring theory has provided us The Laser Interferometer Gravitational Wave Observatory (LIGO) operates with a theoretical laboratory for studying very similar systems of strongly a 40m prototype interferometer on the Caltech campus. The primary interacting hot non-Abelian plasmas. This surprising new perspective mission of the prototype is to serve as an experimental testbed for upgrades extracts the fluid properties of the sQGP from physical processes in a black to the LIGO interferometers and for gaining experience with advanced hole spacetime. Hence we may find the answers to difficult particle physics interferometric techniques, including detuned resonant sideband extraction questions about the sQGP from straightforward calculations in classical (i.e. signal recycling) and dc readout (optical homodyne detection). The general relativity. former technique will be employed in Advanced LIGO, and the latter in both Enhanced and Advanced LIGO. Using dc readout for gravitational wave signal extraction has several technical advantages, including reduced laser and oscillator noise couplings as well as reduced shot noise, when compared to the traditional rf readout technique (optical heterodyne detection) currently in use in large-scale ground-based interferometric gravitational wave detectors. The Caltech 40m laboratory is currently prototyping a dc readout system for a fully suspended interferometric gravitational wave detector. The system includes an optical filter cavity at the interferometer’s output port, and the associated controls and optics to ensure that the filter cavity is optimally coupled to the interferometer. We present the results of measurements to characterize noise couplings in rf and dc readout using this system. Figure 1. Phase diagram of QCD according to theorists [6]. The arrows show caricatures of the evolution of matter in typical RHIC collisions. Figure 2. The dc readout sensing chain. Visible on the table are one PZT steering mirror, the mode-matching telescope, the output mode cleaner (made of copper to damp vibrational modes), the dc photodetectors and other optics.

10 Highlights 2009 Classical and Quantum Gravity

Multipolar analysis of spinning binaries Is quantum gravity necessary? E Berti, V Cardoso, J A González, U Sperhake and B Brügmann S Carlip

2008 Class. Quantum Grav. 25 114035 2008 Class. Quantum Grav. 25 154010

We present a preliminary study of the multipolar structure of gravitational In view of the enormous difficulties we seem to face in quantizing general radiation from spinning black hole binary mergers. We consider three relativity, we should perhaps consider the possibility that gravity is a different spinning binary configurations: (1) one ‘hang-up’ run, where the fundamentally classical interaction. Theoretical arguments against such black holes have equal masses and large spins initially aligned with the mixed classical–quantum models are strong, but not conclusive, and the orbital angular momentum; (2) seven ‘spin-flip’ runs, where the holes have question is ultimately one for experiment. I review some work in progress a mass ratio q  M1/M2 = 4, the spins are anti-aligned with the orbital on the possibility of experimental tests, exploiting the nonlinearity of the angular momentum, and the initial Kerr parameters of the holes j1 = j2 = ji classical–quantum coupling, which could help settle this question. (where j  J/M2) are fine-tuned to produce a Schwarzschild remnant after merger; (3) three ‘super-kick’ runs where the mass ratio q = 1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar Integrability and the AdS/CFT energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin–orbit and spin–spin terms correspondence in a multipolar decomposition of the post-Newtonian waveforms improves N Dorey agreement with the numerical simulation. 2008 Class. Quantum Grav. 25 214003

Intrinsic and fundamental decoherence: In this paper, I review introductory aspects of integrability in the context of the AdS/CFT correspondence. The emergence of integrability and the issues and problems resulting description in terms of factorized scattering are discussed both in C Anastopoulos and B L Hu one-loop gauge theory and in semiclassical string theory.

2008 Class. Quantum Grav. 25 154003 Black holes as effective geometries We investigate the meaning of gravity-induced decoherence in quantum Vijay Balasubramanian, Jan de Boer, Sheer El-Showk and Ilies Messamah theory, known as ‘intrinsic’ or ‘fundamental’ decoherence in the literature. We explore a range of issues relevant to this problem, including the 2008 Class. Quantum Grav. 25 214004 meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific Gravitational entropy arises in string theory via coarse graining over an physical assumptions that enter into different approaches to the subject. underlying space of microstates. In cases with enough supersymmetry, it In particular, we critique two representative approaches that identify time has been possible to explicitly construct such microstates in spacetime and fluctuations as the origin of intrinsic or fundamental decoherence: one that understand how coarse graining of non-singular, horizon-free objects can models the fluctuations by stochastic process and one that purports to lead to an effective description as an extremal black hole. We discuss how derive decoherence from the quantum fluctuations of real clocks. 5 3 4 these results arise in type II string theory on AdS5 × S and on AdS3 × S × T that preserve 16 and eight supercharges, respectively. For such a picture of black holes as effective geometries to extend to cases with a finite Higher-dimensional black holes: hidden horizon area, the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. 2 symmetries and separation of variables By studying examples in M-theory on AdS3 × S × CY that preserve four Valeri P Frolov and David Kubiznˇák supersymmetries, we show how this can happen.

Figure 2. Sketch of a 2008 Class. Quantum Grav. 25 154005 three-centre attractor flow tree from [22, 35]. Lines with arrows indicate single-centre In this paper, we discuss hidden symmetries in rotating black hole attractor flows while spacetimes. We start with an extended introduction which mainly straight lines without summarizes results on hidden symmetries in four dimensions and arrows are walls introduces Killing and Killing–Yano tensors, objects responsible for hidden of marginal stability. The tree starts at the symmetries. We also demonstrate how starting with a principal CKY tensor circle on top (the (that is a closed non-degenerate conformal Killing–Yano 2-form) in 4D moduli at infinity) flat spacetime one can ‘generate’ the 4D Kerr–NUT–(A)dS solution and and flows towards the attractor points its hidden symmetries. After this we consider higher-dimensional Kerr– indicated by the boxes. Note here that Γ4  Γ1  Γ2 and Γ  Γ4  Γ3. On the walls of marginal

NUT–(A)dS metrics and demonstrate that they possess a principal CKY stability the moduli are such that |Z(Γ; t)|  |Z(Γ3; t)|  |Z(Γ4; t)| (horizontal wall on top) and |Z( ; t)|  |Z( ; t)|  |Z( ; t)| (diagonal wall on bottom left). tensor which allows one to generate the whole tower of Killing–Yano and Γ4 Γ1 Γ2 Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton–Jacobi, Klein–Gordon and Dirac equations in the general Kerr–NUT–(A)dS metrics.

Highlights 2009 11 Classical and Quantum Gravity

Fundamental physics with LISA Cosmological particle production in Bernard F Schutz emergent rainbow spacetimes 2009 Class. Quantum Grav. 26 094020 Silke Weinfurtner, Piyush Jain, Matt Visser and C W Gardiner 2009 Class. Quantum Grav. 26 065012 LISA has the potential to make observations that probe deeply into fundamental physics. Not only will it test to exquisite precision the general relativity model for gravitational radiation, but will also test strong-field We investigate cosmological particle production in spacetimes where gravity and in particular the proposition that all black holes are described Lorentz invariance emerges in the infrared limit, but is explicitly broken by the Kerr metric. More research is needed, however, on how to quantify in the ultraviolet regime. Thus these models are similar to many (but not the theoretical meaning of any deviations that might be seen from general all) models of quantum gravity, where a breakdown of Lorentz invariance relativity. LISA can also make important contributions where cosmology and is expected for ultraviolet physics around the Planck/string scale. Our fundamental physics join. LISA’s observations of black-hole coalescences, specific model focuses on the boost subgroup that supports CPT invariance out to redshifts of 20 or more, provide a completely new distance measure, and results in a momentum-dependent dispersion relation. Motivated by one that needs no calibration and is independent of the standard previous studies on spacetimes emerging from a microscopic substrate, cosmological ‘distance ladder’. Using this measure, LISA may even begin to we show how these modifications naturally lead to momentum-dependent measure or limit the time dependence of the dark energy equation of state. rainbow metrics. Firstly, we investigate the possibility of reproducing Beyond these expected results from LISA is the mission’s discovery space: cosmological particle production in spacetimes emerging from real Bose LISA’s high sensitivity raises real possibilities that it will discover sources in gases. Several papers have been written on the analogy between the the dark part of the universe that were completely unexpected. kinematics of linearized perturbations in Bose–Einstein condensates and effective curved-spacetime quantum field theory. Recently we have studied the influence of nonperturbative ultraviolet corrections in time- dependent analog spacetimes, leading to momentum-dependent emergent Highlighted Regular papers rainbow spacetimes. We show that models involving a time-dependent microscopic interaction are suitable for mimicking quantum effects in FRW CQG is primarily an original research journal publishing spacetimes. Within certain limits the analogy is sufficiently good to simulate novel and interesting original research papers in all areas relativistic quantum field theory in time-dependent classical backgrounds, of gravitational physics. All articles are peer reviewed to and the quantum effects are approximately robust against the model- 4 CQG’s usual high standards by 2 independent referees. dependent modifications. Secondly, we analyze how significantly the A selection of top original research papers chosen by particle production process deviates from the common picture. While very the CQG Editorial Board makes up the majority of the low-energy modes do not see the difference at all, some modes ‘re-enter CQG Highlights. the Hubble horizon’ during the inflationary epoch, and extreme ultraviolet modes are completely insensitive to the expansion. The analysis outlined here, because it is nonperturbative in the rainbow metric, exhibits features q that cannot be extracted simply from the standard perturbative modification Cosmology highlights of particle dispersion relations. However, we also show how the final result, after many e-foldings, will approach a time-independent exponentially The radiative transfer at second order: a full decaying particle spectrum. treatment of the Boltzmann equation with polarization Cyril Pitrou

2009 Class. Quantum Grav. 26 065006

This paper investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor-valued distribution function, we study the gauge Figure 6. In this figure, we compare the quasi-particle production per quantum mode (left 4 dependence of the distribution function and summarize the construction column) with its frequency ratio (right column), for ts 1  10 . Parameters are C (¯t  0)  1  105,N  107 and X  2  103. The bold plotted dots on the left-hand of the gauge-invariant distribution function. The Liouville operator which NL 0 side indicate that the frequency ratio is below one, hence the quantum mode corresponds to a describes the free streaming of electrons, and the collision term which super-Hubble horizon mode. While on the right-hand side we indicated with the bold dots when describes the scattering of photons on free electrons are computed up a change in the mode occupation number is above a certain threshold—here ∆Nk 0.004—to filter out quantum noise fluctuations. (a) N (t); (b) R (t); (c) N (t) projected onto the tN to second order. Finally, the remaining dependence in the direction of k k k k plane; (d) Rk (t) projected onto the tRk plane; (e) Nk (t) projected onto the kNk plane; the photon momentum is handled by expanding in projected symmetric (f ) R (t) projected onto the kR plane. trace-free multipoles and also in the more commonly used normal modes k k components. The results obtained remain to be used for computing numerically the contribution in the cosmic microwave background bi- spectrum which arises from the evolution of second-order perturbations, in order to disentangle the primordial non-Gaussianity from the one generated by the subsequent nonlinear evolution.

12 Highlights 2009 Classical and Quantum Gravity

conformal factor which is a function of cosmic time, as well as four example Deformed phase space in a two-dimensional cosmologies for further guidance. Finally, we present our new definitions of minisuperspace model an anisotropic future endless universe and an anisotropic future singularity which offer a promising realization for the new framework. Their irregular, H R Sepangi, B Shakerin and B Vakili degenerate conformal structures differ significantly from those of the isotropic singularity. The combination of the three definitions together could 2009 Class. Quantum Grav. 26 065003 then provide the first complete formalization of the quiescent cosmology concept. For completeness we also present the new definitions of an isotropic future singularity and a future isotropic universe. The relation to We study the effects of noncommutativity and deformed Heisenberg algebra other approaches, in particular to the somewhat dual dynamical systems on the evolution of a two-dimensional minisuperspace cosmological approach, and other asymptotic scenarios is briefly discussed. model in classical and quantum regimes. The phase-space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain Do we live in a ‘small universe’? some approximate analytical solutions for the corresponding classical Ralf Aurich, Holger S Janzer, Sven Lustig and Frank Steiner and quantum cosmology in the presence of the deformed Heisenberg relations between the phase-space variables, in the limit where the 2008 Class. Quantum Grav. 25 125006 minisuperspace variables are small. These results are compared with the standard commutative We compute the effects of a compact flat universe on the angular and noncommutative cases, and correlation function, the angular power spectrum, the circles-in-the-sky similarities and differences of these signature, and the covariance matrix of the spherical harmonics coefficients solutions are discussed. of the cosmic microwave background radiation using the full Boltzmann physics. Our analysis shows that the Wilkinson Microwave Anisotropy Probe Figure 2. The figure on the left shows (WMAP) three-year data are compatible with the possibility that we live in a  2 (u, v) , the square of the commutative 3 3 wavefunction. flat 3-torus with volume −∼ 5 × 10 Gpc .

Closed conformal Killing–Yano tensor and Limitations of anthropic predictions for the the uniqueness of generalized Kerr–NUT– cosmological constant Λ: cosmic heat death de Sitter spacetime of anthropic observers Tsuyoshi Houri, Takeshi Oota and Yukinori Yasui Laura Mersini–Houghton and Fred C Adams

2009 Class. Quantum Grav. 26 045015 2008 Class. Quantum Grav. 25 165002

The higher-dimensional Kerr–NUT–de Sitter spacetime describes the This paper investigates anthropic bounds on the vacuum energy Λ by general rotating asymptotically de Sitter black hole with NUT parameters. considering alternate starting assumptions. We first consider the possibility It is known that such a spacetime possesses a rank-2 closed conformal of cosmic observers existing at any random time (including the future) Killing–Yano (CKY) tensor as a ‘hidden’ symmetry which provides the for constant Λ, and take into account the suppression of new structure separation of variables for the geodesic equations and Klein–Gordon formation as the universe approaches its eternal de Sitter (DS) geometry. equations. We present a classification of higher-dimensional spacetimes Structures that collapse prior to the era of Λ-domination will lose causal admitting a rank-2 closed CKY tensor. This provides a generalization of the contact with our Hubble volume within a finite (short) conformal time τ∗. Kerr–NUT–de Sitter spacetime. In particular, we show that the Kerr–NUT–de Any remnants within our Hubble volume then suffer a cosmological heat Sitter spacetime is the only spacetime with a non-degenerate CKY tensor. death after the universe becomes DS. The probability for finding observers by random measurements in the volume bound by the de Sitter horizon

is proportional to the rate of change in the ratio of the 3-volume V3(τ) to

the 4-volume V4(τ), so that P −∼ 0. This vanishing probability of populated Encoding cosmological futures with DS volumes is a simple consequence of the information loss problem for eternal DS spaces resulting from the finite and constant value of its −½ conformal structures temperature TDS −∼ Λ and entropy S = 3/(GΛ). By contrast, for geometries Philipp A Höhn and Susan M Scott with Λ = 0, structures can condense and entropy production can continue without bounds at any epoch. The probability of finding observers in Λ = 0 2009 Class. Quantum Grav. 26 035019 geometries is thus overwhelming higher than in DS spaces. As a result, anthropic reasoning does not explain the small but nonzero vacuum energy observed in our universe. We also address the case where observers are Quiescent cosmology and the Weyl curvature hypothesis possess a considered only at a specially chosen time—like the present epoch—but mathematical framework, namely the definition of an isotropic singularity, relax the allowed values of starting density fluctuations and hence the but only for the initial state of the universe. A complementary framework redshift of galaxy formation. In this latter case, the bounds on a Λ can be is necessary to also encode appropriate cosmological futures. In order to millions of times larger than previous estimates—and the observed value. devise a new framework we analyse the relation between regular conformal We thus conclude that anthropic reasoning has limited predictive power. structures and (an)isotropy, the behaviour and role of a monotonic

Highlights 2009 13 Classical and Quantum Gravity

On the curvature of the present-day universe First joint search for gravitational-wave bursts Thomas Buchert and Mauro Carfora in LIGO and GEO 600 data 2008 Class. Quantum Grav. 25 195001 B Abbott et al (for the LIGO Scientific Collaboration) 2008 Class. Quantum Grav. 25 245008 We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the We present the results of the first joint search for gravitational-wave bursts question of whether it is sensible to assume that curvature averages out by the LIGO and GEO 600 detectors. We search for bursts with characteristic on some scale of homogeneity, as implied by the standard concordance central frequencies in the band 768–2048 Hz in the data acquired between model of cosmology, or whether the averaged scalar curvature can be 22 February and 23 March, 2005 (fourth LSC Science Run–S4). We discuss largely negative today, as required for an explanation of dark energy from the inclusion of the GEO 600 data in the Waveburst–CorrPower pipeline inhomogeneities. We confront both conjectures with a detailed analysis that first searches for coincident excess power events without taking into of the kinematical backreaction term and estimate its strength for a account differences in the antenna responses or strain sensitivities of the multi-scale inhomogeneous matter and curvature distribution. Our main various detectors. We compare the performance of this pipeline to that of result is a formula for the spatially averaged scalar curvature involving the coherent Waveburst pipeline based on the maximum likelihood statistic. quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. This likelihood statistic is derived from a coherent sum of the detector data We propose strategies to quantitatively evaluate the formula, and pinpoint streams that takes into account the antenna patterns and sensitivities of the assumptions implied by the conjecture of a small or zero averaged the different detectors in the network. We find that the coherent Waveburst curvature. We reach the conclusion that the standard concordance model pipeline is sensitive to signals of amplitude 30–50% smaller than the needs fine tuning in the sense of an assumed equipartition law for curvature Waveburst–CorrPower pipeline. We perform a search for gravitational-wave in order to reconcile it with the estimated properties of the averaged bursts using both pipelines and find no detection candidates in the S4 data physical space, whereas a negative averaged curvature is favoured, set when all four instruments were operating stably. independent of the prior on the value of the cosmological constant.

Figure 12. A pictorial representation of the (longitudinal) shear generated Experimental investigation of a control on a small sphere by three (independent) eigenvectors  scheme for a zero-detuning resonant  (i) i1,2,3, associated with the

first (degenerate) eigenvalue 1 of a sideband extraction interferometer for the vector Laplacian ∆h. Such eigenvectors define a moving frame in which the shear is, in a L2-average next-generation gravitational-wave detectors sense, minimized. The region of near Fumiko Kawazoe et al homogeneity D can be defined as the largest region in (, g) where we can introduce such minimal 2008 Class. Quantum Grav. 25 195008 shear eigenvectors.

Some next-generation gravitational-wave detectors, such as the American Advanced LIGO project and the Japanese LCGT project, plan to use power recycled resonant sideband extraction (RSE) interferometers for their q Experimental gravity highlights interferometer’s optical configuration. A power recycled zero-detuning (PRZD) RSE interferometer, which is the default design for LCGT, has five main length degrees of freedom that need to be controlled in order to C-readout of a signal-recycled gravitational operate a gravitational-wave detector. This task is expected to be very challenging because of the complexity of optical configuration. A new wave detector control scheme for a PRZD RSE interferometer has been developed and S Hild et al tested with a prototype interferometer. The PRZD RSE interferometer was successfully locked with the control scheme. It is the first experimental 2009 Class. Quantum Grav. 26 055012 demonstration of a PRZD RSE interferometer with suspended test masses. The result serves as an important step for the operation of LCGT.

Figure 4. l error All first-generation large-scale gravitational wave detectors are operated at signal with SEM free the dark fringe and use a heterodyne readout employing radio frequency and l in lock. (RF) modulation–demodulation techniques. However, the experience in the currently running interferometers reveals several problems connected with a heterodyne readout, of which phase noise of the RF modulation is the most serious one. A homodyne detection scheme (DC-readout), using the highly stabilized and filtered carrier light as a local oscillator for the readout, is considered to be a favourable alternative. Recently a DC-readout scheme has been implemented on the GEO 600 detector. We describe the results of first measurements and give a comparison of the performance achieved with homodyne and heterodyne readout. The implications of the combined use of DC-readout and signal recycling are considered.

14 Highlights 2009 Classical and Quantum Gravity

Search for gravitational waves associated q Mathematical general relativity highlights with GRB 050915a using the Virgo detector F Acernese et al Mixmaster: fact and belief J Mark Heinzle and Claes Uggla 2008 Class. Quantum Grav. 25 225001 2009 Class. Quantum Grav. 26 075016

In the framework of the expected association between gamma-ray bursts and gravitational waves, we present results of an analysis aimed to search We consider the dynamics towards the initial singularity of Bianchi type for a burst of gravitational waves in coincidence with gamma-ray burst IX vacuum and orthogonal perfect fluid models with a linear equation of 050915a. This was a long duration gamma-ray burst detected by Swift state. Surprisingly few facts are known about the ‘Mixmaster’ dynamics of during September 2005, when the Virgo gravitational wave detector was these models, while at the same time most of the commonly held beliefs engaged in a commissioning run during which the best sensitivity attained are rather vague. In this paper, we use Mixmaster facts as a base to build an in 2005 was exhibited. This offered the opportunity for Virgo’s first search infrastructure that makes it possible to sharpen the main Mixmaster beliefs. for a gravitational wave signal in coincidence with a gamma-ray burst. The We formulate explicit conjectures concerning (i) the past asymptotic states result of our study is a set of strain amplitude upper limits, based on the of type IX solutions and (ii) the relevance of the Mixmaster/Kasner map loudest event approach, for different but quite general types of burst signal for generic past asymptotic dynamics. The evidence for the conjectures is waveforms. The best upper limit strain amplitudes we obtain are based on a study of the stochastic properties of this map in conjunction with –20 −1/2 hrss = O(10 ) Hz around ~200–1500 Hz. These upper limits allow us to dynamical systems techniques. We use a dynamical systems formulation, evaluate the level up to which Virgo, when reaching nominal sensitivity, will since this approach has so far been the only successful path to obtain be able to constrain the gravitational wave output associated with a long theorems, but we also make comparisons with the ‘metric’ and Hamiltonian burst. Moreover, the analysis presented here plays the role of a prototype, ‘billiard’ approaches. crucial in defining a methodology for gamma-ray burst triggered searches with Virgo and opening the way for future joint analyses with LIGO.

Gravitational radiation from pulsar glitches C A van Eysden and A Melatos

2008 Class. Quantum Grav. 25 225020

The nonaxisymmetric Ekman flow excited inside a neutron star following a rotational glitch is calculated analytically including stratification and compressibility. For the largest glitches, the gravitational wave strain produced by the hydrodynamic mass quadrupole moment approaches the sensitivity range of advanced long-baseline interferometers. It is shown that the viscosity, compressibility and orientation of the star can be inferred Figure 6. Concatenating type II transition orbits we obtain sequences of transitions—heteroclinic chains. The discrete map governing the associated sequence of fixed points on K is the in principle from the width and amplitude ratios of the Fourier peaks (at Mixmaster map. The arrows indicate the direction of time toward the past. the spin frequency and its first harmonic) observed in the gravitational wave spectrum in the + and × polarizations. These transport coefficients constrain the equation of state of bulk nuclear matter, because they depend sensitively on the degree of superfluidity. Regularity of the Einstein equations at future null infinity Vincent Moncrief and Oliver Rinne

2009 Class. Quantum Grav. 26 125010

When Einstein’s equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal factor and thus appear to be ill-behaved at this (exterior) boundary. In this paper however we show, through an enforcement of the Hamiltonian and momentum constraints to the needed order in a Taylor expansion, that these apparently singular terms are not only regular at the boundary but can in fact be explicitly evaluated there in terms of conformally regular geometric data. Though we employ a rather Figure 6. Width and amplitudes for the gravitational wave spectrum seen by a polar observer rigidly constrained and gauge-fixed formulation of the field equations, we showing the effect of buoyancy and stratification. discuss the extent to which we expect our results to have a more ‘universal’ significance and, in particular, to be applicable, after minor modifications, to alternative formulations.

Highlights 2009 15 Classical and Quantum Gravity

A rigorous derivation of gravitational The third post-Newtonian gravitational wave self-force polarizations and associated spherical Samuel E Gralla and Robert M Wald harmonic modes for inspiralling compact 2008 Class. Quantum Grav. 25 205009 binaries in quasi-circular orbits Luc Blanchet, Guillaume Faye, Bala R Iyer and Siddhartha Sinha There is general agreement that the MiSaTaQuWa equations should describe the motion of a ‘small body’ in general relativity, taking into 2008 Class. Quantum Grav. 25 165003 account the leading order self-force effects. However, previous derivations of these equations have made a number of ad hoc assumptions and/ or contain a number of unsatisfactory features. For example, all previous The gravitational waveform (GWF) generated by inspiralling compact derivations have invoked, without proper justification, the step of ‘Lorenz binaries moving in quasi-circular orbits is computed at the third gauge relaxation’, wherein the linearized Einstein equation is written in the post-Newtonian (3PN) approximation to general relativity. Our motivation form appropriate to the Lorenz gauge, but the Lorenz gauge condition is is two-fold: (i) to provide accurate templates for the data analysis of then not imposed—thereby making the resulting equations for the metric gravitational wave inspiral signals in laser interferometric detectors; (ii) to perturbation inequivalent to the linearized Einstein equations. (Such a provide the associated spin-weighted spherical harmonic decomposition ‘relaxation’ of the linearized Einstein equations is essential in order to avoid to facilitate comparison and match of the high post-Newtonian prediction the conclusion that ‘point particles’ move on geodesics.) In this paper, we for the inspiral waveform to the numerically-generated waveforms for the analyze the issue of ‘particle motion’ in general relativity in a systematic merger and ringdown. This extension of the GWF by half a PN order (with and rigorous way by considering a one-parameter family of metrics, respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation gab(λ), corresponding to having a body (or black hole) that is ‘scaled down’ to zero size and mass in an appropriate manner. We prove that the of the relations between the radiative, canonical and source multipole limiting worldline of such a one-parameter family must be a geodesic of moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, the background metric, gab(λ = 0). Gravitational self-force—as well as the force due to coupling of the spin of the body to curvature—then arises as and compute the contributions of hereditary terms (tails, tails-of-tails and a first-order perturbative correction in λ to this worldline. No assumptions memory integrals) up to 3PN order. The end results are given for both the are made in our analysis apart from the smoothness and limit properties of complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes. the one-parameter family of metrics, gab(λ). Our approach should provide a framework for systematically calculating higher order corrections to gravitational self-force, including higher multipole effects, although we do not attempt to go beyond first-order calculations here. The status of the MiSaTaQuWa equations is explained. q Black holes highlights Symmetries of higher dimensional q Numerical relativity highlights black holes Vincent Moncrief and James Isenberg Constrained evolution in axisymmetry and the 2008 Class. Quantum Grav. 25 195015 gravitational collapse of prolate Brill waves Oliver Rinne We prove that if a stationary, real analytic, asymptotically flat vacuum black 2008 Class. Quantum Grav. 25 135009 hole spacetime of dimension n ≥ 4 contains a non-degenerate horizon with compact cross-sections that are transverse to the stationarity generating Killing vector field then, for each connected component of the black hole’s This paper is concerned with the Einstein equations in axisymmetric vacuum horizon, there is a Killing field which is tangent to the generators of the spacetimes. We consider numerical evolution schemes that solve the horizon. For the case of rotating black holes, the stationarity generating constraint equations as well as elliptic gauge conditions at each time step. Killing field is not tangent to the horizon generators and therefore the We examine two such schemes that have been proposed in the literature isometry group of the spacetime is at least two dimensional. Our proof and show that some of their elliptic equations are indefinite, thus potentially relies on significant extensions of our earlier work on the symmetries of admitting nonunique solutions and causing numerical solvers based on spacetimes containing a compact Cauchy horizon, allowing now for classical relaxation methods to fail. A new scheme is then presented that non-closed generators of the horizon. does not suffer from these problems. We use our numerical implementation to study the gravitational collapse of Brill waves. A highly prolate wave is shown to form a black hole rather than a naked singularity.

DID YOU KNOW? ...if you have source code relating to your computational work, you can now publish that code for free in CQG’s Published Software Archive? Published codes will remain freely available for perpetuity. See the CQG website for more details iopscience.org/cqg. Luis Lehner, Classical and Quantum Gravity Editorial Board Member

16 Highlights 2009 Classical and Quantum Gravity

The thermodynamics of Kaluza–Klein black q Quantum cosmology highlights hole/bubble chains David Kastor, Sourya Ray and Jennie Traschen Are loop quantum cosmos never singular? Parampreet Singh 2008 Class. Quantum Grav. 25 125004 2009 Class. Quantum Grav. 26 125005

A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr A unified treatment of all known types of singularities for flat, isotropic relations and the mass and tension first laws for spacetimes containing and homogeneous spacetimes in the framework of loop quantum both black holes and Killing bubbles. The resulting relations display an cosmology (LQC) is presented. These include bangs, crunches and all interesting interchange symmetry between the properties of black hole future singularities. Using effective spacetime description we perform horizons and those of KK bubbles. This interchange symmetry reflects the a model-independent general analysis of the properties of curvature, underlying relation between static bubbles and black holes under double behavior of geodesics and strength of singularities. For illustration purposes analytic continuation of the time and Kaluza–Klein directions. The a phenomenological model based analysis is also performed. We show thermodynamics of bubbles involve a geometrical quantity that we call that all values of the scale factor at which a strong singularity may occur the bubble surface gravity, which we show has several properties in are excluded from the effective loop quantum spacetime. Further, if the common with the black hole surface gravity. evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exists a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives Uniqueness of near-horizon geometries of will always diverge. Such events however turn out to be harmless weak curvature singularities beyond which geodesics can be extended. Our rotating extremal AdS4 black holes results point toward a generic resolution of physical singularities in LQC. Hari K Kunduri and James Lucietti

2009 Class. Quantum Grav. 26 055019 Quantum-mechanical breakdown of perfect We consider stationary extremal black hole solutions of the Einstein– homogeneity in reheating after inflation Maxwell equations with a negative cosmological constant in four Ali Kaya dimensions. We determine all non-static axisymmetric near-horizon geometries and all static near-horizon geometries for black holes of this 2009 Class. Quantum Grav. 26 045017 kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS4 rotating extremal black hole is the near-horizon limit of extremal Kerr–Newman–AdS . We also identify the 4 In the context of quantum fields in time-dependent classical backgrounds, subset of near-horizon geometries which are supersymmetric. Finally, we we note that the number of created particles with a given momentum show which physical quantities of extremal black holes may be computed largely deviates about its mean value. Guided with this observation we from the near-horizon limit alone, and point out a simple formula for the use a complete orthonormal family of localized wave packets to calculate entropy of the known supersymmetric AdS black hole. Analogous results 4 the deviations in the number and energy densities of particles produced are presented in the case of a vanishing cosmological constant. in a volume of a given size during reheating. It turns out that at the end of reheating there exist (in general tiny) spatial variations in these densities on Hubble length scales over which local interactions are incapable of restoring homogeneity. This signals the destruction of perfect homogeneity Hawking radiation of Dirac particles via attained after inflation due to the quantum nature of the particle production tunneling from the Kerr black hole process in reheating. Ran Li, Ji-Rong Ren and Shao-Wen Wei 2008 Class. Quantum Grav. 25 125016 Quantum deformations of Schwarzschild and Schwarzschild–de Sitter spacetimes We investigated Dirac particles’ Hawking radiation from the event horizon Ding Wang, R B Zhang and Xiao Zhang of the Kerr black hole in terms of the tunneling formalism. Applying the WKB approximation to the general covariant Dirac equation in the Kerr spacetime 2009 Class. Quantum Grav. 26 085014 background, we obtain the tunneling probability for fermions and Hawking temperature of the Kerr black hole. The result obtained by taking the fermion tunneling into account is consistent with the previous literature. A quantum Schwarzschild spacetime and a quantum Schwarzschild–de Sitter spacetime with a cosmological constant Λ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The metrics and curvatures of the quantum Schwarzschild spacetime and the quantum Schwarzschild–de Sitter spacetime are computed. It is shown that up to the second order in the deformation parameter, the quantum spacetimes are solutions of a noncommutative Einstein equation.

Highlights 2009 17 Classical and Quantum Gravity

On the resolution of the big bang singularity Arithmetical chaos and quantum cosmology in isotropic loop quantum cosmology L A Forte Madhavan Varadarajan 2009 Class. Quantum Grav. 26 045001 2009 Class. Quantum Grav. 26 085006 In this paper, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux In contrast to previous work in the field, we construct the loop quantum and Nicolai in the study of the cosmological singularity. In particular we cosmology (LQC) of the flat isotropic model with a massless scalar field in use the theory of Maass automorphic forms and recent mathematical the absence of higher order curvature corrections to the gravitational part results about arithmetical dynamical systems. The predictions of the of the Hamiltonian constraint. The matter part of the constraint contains billiard model give precise automorphic properties for the wavefunction the inverse triad operator which can be quantized with or without the (Maass–Hecke eigenform), the asymptotic number of quantum states use of a Thiemann-like procedure. With the latter choice, we show that (Selberg asymptotics for PSL (2, Ζ), the distribution for the level spacing the LQC quantization is identical to that of the standard Wheeler–DeWitt statistics (the Poissonian one) and the absence of scarred states. The most theory (WDW) wherein there is no singularity resolution. We argue that the interesting implication of this model is perhaps that the discrete spectrum is former choice leads to singularity resolution in the sense of a well-defined, fully embedded in the continuous one. regular (backward) evolution through and beyond the epoch where the size of the universe vanishes. Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three ‘exotic’ structures in this LQC model, namely: Quantum cosmological Friedman models curvature corrections, inverse triad definitions and the ‘polymer’ nature of the kinematic representation. We also critically examine certain technical with an initial singularity assumptions made by APS in their analysis of WDW semiclassical states Claus Gerhardt and point out some problems stemming from the infrared behaviour of their wavefunctions. 2009 Class. Quantum Grav. 26 015008

We consider the Wheeler–DeWitt equation Hψ = 0 in a suitable Hilbert Physical time and other conceptual issues space. It turns out that this equation has countably many solutions ψ, of quantum gravity on the example of loop which can be considered as eigenfunctions of a Hamilton operator implicitly defined by H. We consider two models, a bounded one, 0 < r < r0, and an quantum cosmology unbounded, 0 < r < ∞, which represent different eigenvalue problems. In the bounded model we look for eigenvalues Λ, where the Λ are the Wojciech Kamin´ski, Jerzy Lewandowski and Tomasz Pawłowski i i values of the cosmological constant which we used in the Einstein–Hilbert functional, and in the unbounded model the eigenvalues are given by 2009 Class. Quantum Grav. 26 035012 n − 1 ()−−Ki n

Several conceptual aspects of quantum gravity (QG) are studied on the where Λi < 0. Note that r is the symbol for the scale factor, usually denoted example of the homogeneous isotropic loop quantum cosmology (LQC) by a, or a power of it. The ψ form a basis of the underlying Hilbert space. We model. In particular: (i) the proper time of the comoving observers is shown prove furthermore that the implicitly defined Hamilton operator is selfadjoint to be a quantum operator and a quantum spacetime metric tensor operator and that the solutions of the corresponding Schrödinger equation satisfy is derived. (ii) Solutions of the quantum scalar constraint for two different the Wheeler–DeWitt equation, if the initial values are superpositions of choices of the lapse function are compared and contrasted. In particular eigenstates. All solutions have an initial singularity in r = 0. Under certain it is shown that in the case of a model with massless scalar field and circumstances a smooth transition from big crunch to big bang is possible. cosmological constant Λ, the physical Hilbert spaces constructed for two choices of lapse are the same for Λ < 0 while they are significantly different for Λ > 0. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator, whose essential spectrum was shown to be an interval [0, ρcr], where ρcr ≈ 0.41 ρPI. (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables.

Look out for the special CQG Cluster Issue on Non-linear Cosmological Perturbations to be published in the Summer of 2010. This cluster issue is not based on any conference, but is instead a collection of specially chosen high-quality articles in a rapidly developing sub-field of Cosmology. Articles in this special issue will be made free to download for 6 months from their date of online publication. David Wands and Misao Sasaki, Editors of the Nonlinear Cosmological Perturbations Cluster issue

18 Highlights 2009 Classical and Quantum Gravity

Effective actions from loop quantum q Quantum gravity highlights cosmology: correspondence with higher What is a particle? curvature gravity Daniele Colosi and Carlo Rovelli Ghanashyam Date and Sandipan Sengupta 2009 Class. Quantum Grav. 26 025002 2009 Class. Quantum Grav. 26 105002

Theoretical developments related to gravitational interaction have Quantum corrections of certain types and relevant in certain regimes can questioned the notion of particle in quantum field theory (QFT). For be summarized in terms of an effective action calculable, in principle, from instance, uniquely defined particle states do not exist in general, in QFT the underlying theory. The demands of symmetries, local form of terms on a curved spacetime. More generally, particle states are difficult to and dimensional considerations limit the form of the effective action to a define in a background-independent quantum theory of gravity. These great extent leaving only the numerical coefficients to distinguish different difficulties have led some to suggest that in general QFT should not be underlying theories. The effective action can be restricted to particular interpreted in terms of particle states, but rather in terms of eigenstates of symmetry sectors to obtain the corresponding, reduced effective action. local operators. Still, it is not obvious how to reconcile this view with the Alternatively, one can also quantize a classically (symmetry) reduced theory empirically-observed ubiquitous particle-like behavior of quantum fields, and obtain the corresponding effective action. These two effective actions apparent for instance in experimental high-energy physics, or ‘particle’ can be compared. As an example, we compare the effective action(s) physics. Here we offer an element of clarification by observing that already known in isotropic loop quantum cosmology with the Lovelock actions, as in flat space there exist—strictly speaking—two distinct notions of particles: well as with more general actions, specialized to homogeneous isotropic globally defined n-particle Fock-states and local particle states. The last spacetimes and find that the m¯-scheme is singled out. describes the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance A simplified quantum gravitational model of for flat-space theories—it amounts to a reminder that there are boundary effects in realistic detectors—but is relevant for gravity. It reconciles the inflation two points of view mentioned above. More importantly, it provides a N C Tsamis and R P Woodard definition of the local particle state that remains well defined even when the conventional global particle states are not defined. This definition plays an 2009 Class. Quantum Grav. 26 105006 important role in quantum gravity.

Inflationary quantum gravity simplifies drastically in the leading logarithm approximation. We show that the only counterterm which contributes in this limit is the 1-loop renormalization of the cosmological constant. We Path integral representation of spin foam go further to make a simplifying assumption about the operator dynamics models of 4D gravity at leading logarithm order. This assumption is explicitly implemented Florian Conrady and Laurent Freidel at 1- and 2-loop orders, and we describe how it can be implemented nonperturbatively. We also compute the expectation value of an invariant 2008 Class. Quantum Grav. 25 245010 observable designed to quantify the quantum gravitational back-reaction on inflation. Although our dynamical assumption may not prove to be completely correct, it does have the right time dependence, it can naturally We give a unified description of all recent spin foam models introduced by produce primordial perturbations of the right strength, and it illustrates how Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). a rigorous application of the leading logarithm approximation might work in We show that the FK models are, for all values of the Immirzi parameter γ, quantum gravity. It also serves as a partial test of the ‘null hypothesis’ that equivalent to path integrals of a discrete theory and we provide an explicit there are no significant effects from infrared gravitons. formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov’s and Livine’s SO(4) projected states. For 0  γ  1, the states can be restricted to Consistent loop quantum cosmology SU(2) spin networks. Martin Bojowald

2009 Class. Quantum Grav. 26 075020

A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an isotropic universe filled with a free, massless scalar field would bounce must be well below the Planck density. In the presence of anisotropy, no model of the Schwarzschild black hole interior analyzed so far is consistent. Figure 1. (a) Face f of dual complex ∆*. (b) Subdivision of face f into wedges. The arrows indicate starting point and orientation for wedge holonomies.

Highlights 2009 19 Classical and Quantum Gravity q Strings, branes, supergravity and Excited states of a string in a time-dependent gauge theory highlights orbifold Przemysław Małkiewicz and Włodzimierz Piechocki Supersymmetric multi-trace boundary 2009 Class. Quantum Grav. 26 015008 conditions in AdS Aaron J Amsel and Donald Marolf We present analytical results on 2009 Class. Quantum Grav. 26 025010 the propagation of a classical string in nonzero modes through the singularity of the compactified

Boundary conditions for massive fermions are investigated in AdSd for Milne space. We restrict our d ≥ 2. For fermion masses in the range 0 ≤ |m| < 1/2l with l being analysis to a string winding the AdS length, the standard notion of normalizeability allows a choice around the compact dimension of of boundary conditions. As in the case of scalars at or slightly above spacetime. The compact dimension the Breitenlohner–Freedman (BF) bound, such boundary conditions undergoes contraction to a point correspond to multi-trace deformations of any CFT dual. By constructing followed by re-expansion. We appropriate boundary superfields, for d = 3, 4, 5 we identify joint scalar/ demonstrate that the classical fermion boundary conditions which preserve either N = 1 supersymmetry or dynamics of the string in excited N = 1 superconformal symmetry on the boundary. In particular, we identify states is non-singular in the entire boundary conditions corresponding via AdS/CFT (at large N) to a 595- spacetime. parameter family of double-trace marginal deformations of the low-energy theory of N M2-branes which preserve N = 1 superconformal symmetry. We Figure 1. Compactified 2D Milne space embedded in 3D Minkowski space. also establish that (at large N and large ‘t Hooft coupling λ) there are no marginal or relevant multi-trace deformations of 3+1 N = 4 super Yang–Mills which preserve even N = 1 supersymmetry. The Newman–Penrose formalism in higher dimensions: vacuum spacetimes with a Squashing gravity dual of N = 6 non-twisting geodetic multiple Weyl aligned superconformal Chern–Simons gauge theory Changhyun Ahn null direction A Pravdová and V Pravda 2009 Class. Quantum Grav. 26 105001 2008 Class. Quantum Grav. 25 235008

Four-dimensional field equations are determined for perturbations of the quotient 7-sphere size and squashing parameter in 11-dimensional Vacuum spacetimes admitting a non-twisting geodetic multiple Weyl supergravity. The quotient 7-sphere is an S1-bundle over the CP3 which aligned null direction (WAND) are analysed in arbitrary dimension using a 2 4 is regarded as an S -fibration over the base S . By analyzing the AdS4 recently developed higher-dimensional Newman–Penrose (NP) formalism. supergravity scalar potential, the holographic supersymmetric (or We determine the dependence of the metric and of the Weyl tensor on the nonsupersymmetric) renormalization group (RG) flow from N = 1 (or affine parameter r along null geodesics generated by the WAND for type

N = 0) SO(5) × U(1)-invariant UV fixed point to N = 6 (or N = 0) SU(4)R × III and N spacetimes and for a special class of type II and D spacetimes, U(1)-invariant IR fixed point is obtained. The three-dimensional boundary containing e.g. Schwarzschild–Tangherlini black holes and black strings theories are described by superconformal Chern–Simons matter theories and branes. For types III and N, all metric components are at most quadratic and a dual operator corresponding to this RG flow is described. polynomials in r while for types II and D the r-dependence of the metric as well as of the Weyl tensor is determined by an integer m corresponding

to the rank of the expansion matrix Sij. It is shown that for non-vanishing expansion, all these spacetimes contain a curvature singularity. As an Light-cone M5 and multiple M2-branes illustrative example, a shearing expanding type N five-dimensional vacuum Igor A Bandos and Paul K Townsend solution is also re-derived using higher-dimensional NP formalism. This solution can be, however, identified with a direct product of a known four- 2008 Class. Quantum Grav. 25 245003 dimensional type N metric with an extra dimension.

We present the light-cone gauge fixed Lagrangian for the M5-brane; it has a residual ‘exotic’ gauge invariance with the group of 5-volume preserving diffeomorphisms, SDiff5, as gauge group. For an M5-brane of topology DID YOU KNOW? R2 × M , for closed 3-manifold M , we find an infinite tension limit that 3 3 CQG is one of the most selective journals in the field? yields an SO(8)-invariant (1 + 2)-dimensional field theory with ‘exotic’ SDiff3 gauge invariance. We show that this field theory is the Carrollian limit of the CQG accepted 40.7% of regular submissions to the journal Nambu bracket realization of the ‘BLG’ model for multiple M2-branes. in 2009, ensuring that only internationally competitive papers of a very high quality are to be found in CQG.

20 Highlights 2009 Classical and Quantum Gravity

On the maximal superalgebras of Non-existence of asymptotically flat geons supersymmetric backgrounds in (2 + 1) gravity José Figueroa-O’Farrill, Emily Hackett-Jones, George Moutsopoulos and Kory A Stevens, Kristin Schleich and Donald M Witt Joan Simón 2009 Class. Quantum Grav. 26 075012 2009 Class. Quantum Grav. 26 035016

Geons, small topological structures that exhibit particle properties such as In this paper we give a precise definition of the notion of a maximal charge and angular momentum without the presence of matter sources, superalgebra of certain types of supersymmetric supergravity backgrounds, have been extensively discussed in (3 + 1)-dimensional general relativity. including the Freund–Rubin backgrounds, and propose a geometric Given the recent renewal of interest in (2 + 1) gravity, it is natural to ask construction extending the well-known construction of its Killing whether or not the notion of geons extends to three dimensions. We prove superalgebra. We determine the structure of maximal Lie superalgebras here that, in contrast to the (3 + 1)-dimensional case, there are no (2 + and show that there is a finite number of isomorphism classes, all 1)-dimensional asymptotically flat solutions of the vacuum Einstein or related via contractions from an orthosymplectic Lie superalgebra. We Einstein–Maxwell equations containing geons. In contrast, (2 + 1)- use the structure theory to show that maximally supersymmetric waves dimensional asymptotically anti-de Sitter spacetimes can indeed contain do not possess such a maximal superalgebra, but that the maximally geons; however, the geons are always hidden behind a single black hole supersymmetric Freund–Rubin backgrounds do. We perform the explicit horizon. We also prove sufficient conditions for the non-existence of (2 + 7 1)-dimensional asymptotically flat geon-containing solutions. geometric construction of the maximal superalgebra of AdS4 × S and find that it is isomorphic to osp(132). We propose an algebraic construction of 7 the maximal superalgebra of any background asymptotic to AdS4 × S and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement. Approximate spacetime symmetries and conservation laws Abraham I Harte q Geometry and topology highlights 2008 Class. Quantum Grav. 25 205008 Projective equivalence of Einstein spaces A notion of geometric symmetry is introduced that generalizes the classical in general relativity concepts of Killing fields and other affine collineations. There is a sense G S Hall and D P Lonie in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations 2009 Class. Quantum Grav. 26 125009 that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincaré and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these There has been some recent interest in the relation between two spacetimes objects are discussed for both geodesics and extended matter distributions. which have the same geodesic paths, that is, spacetimes which are One example is a generalized Komar integral that may be taken to define projectively equivalent (sometimes called geodesically equivalent). This the linear and angular momenta of a spacetime volume as seen by a paper presents a short and accessible proof of the theorem that if two particular observer. This is evaluated explicitly for a gravitational plane wave spacetimes have the same geodesic paths and one of them is an Einstein spacetime. space then (either each is of constant curvature or) their Lévi-Civitá connections are identical. It also clarifies the relationship between their associated metrics. The results are extended to include the signatures (+ + + +) and (− − + +), and some examples and discussion are given in the case of dimension n > 4. Some remarks are also made which show how these results may be useful in the study of projective symmetry. IOPscience express on your iPhone Keep up to date with the latest On static n-body configurations in relativity articles published in IOP journals Search Robert Beig and Richard M Schoen • • Read Download 2009 Class. Quantum Grav. 26 075014 • • E-mail

The static n-body problem of general relativity states that there are, under a reasonable energy condition, no static n-body configurations for n > 1, iopscience.org provided the configuration of the bodies satisfies a suitable separation condition. In this paper we solve this problem in the case that there exists a closed, noncompact, totally geodesic surface disjoint from the bodies. This covers the situation where the configuration has a reflection symmetry across a noncompact surface disjoint from the bodies.

Highlights 2009 21 Classical and Quantum Gravity

Rigid motion revisited: rigid quasilocal frames Applications of the Gauss–Bonnet theorem Richard J Epp, Robert B Mann and Paul L McGrath to gravitational lensing 2009 Class. Quantum Grav. 26 035015 G W Gibbons and M C Werner 2008 Class. Quantum Grav. 25 235009 In this first of a series of papers we will introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a ‘system’ in the context of the dynamical spacetime of general relativity. An RQF is In this geometrical approach to gravitational lensing theory, we apply defined as a two-parameter family of timelike worldlines comprising the the Gauss–Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak worldtube boundary (topologically R × S2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is deflection limit. We find that the focusing of the light rays emerges here expansion-free (the ‘size’ of the system is not changing) and shear-free as a topological effect, and we introduce a new method to calculate the (the ‘shape’ of the system is not changing). This definition of a system is deflection angle from the Gaussian curvature of the optical metric. As anticipated to yield simple, exact geometrical insights into the problem of examples, the Schwarzschild lens, the Plummer sphere and the singular motion in general relativity. It begins by answering, in a precise way, the isothermal sphere are discussed within this framework. questions of what is in motion (a rigid two-dimensional system boundary Figure 1. Weak deflection lensing 2 with topology S , and whatever matter and/or radiation it happens to geometry. Two geodesics 1 and  from the source S to the contain at the moment), and what motions of this rigid boundary are 2 observer O are deflected by a lens possible. Nearly a century ago Herglotz and Noether showed that a three- with centre at L. D1 and D2 are two parameter family of timelike worldlines in Minkowski space satisfying Born’s domains with boundary curves L  1909 rigidity conditions does not have the 6 degrees of freedom we are and D as discussed in the text. familiar with from Newtonian mechanics, but a smaller number—essentially only 3. This result curtailed, to a large extent, subsequent study of rigid motion in special and (later) general relativity. We will argue that in fact we can implement Born’s notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers)—with precisely the expected 3 translational and 3 rotational degrees of freedom (with arbitrary time q Comments, Replies and Notes highlights dependence)—provided the system is defined quasilocally as the two-dimensional set of A note on non-compact Cauchy surfaces points comprising the boundary Do-Hyung Kim of a finite spatial volume, rather than the three-dimensional set 2008 Class. Quantum Grav. 25 238002 of points within the volume.

Figure 1. The shape of the rotating It is shown that if a spacetime has a non-compact Cauchy surface Σ, then observers’ round sphere as seen by observers in the inertial reference frame: its causal structure is completely determined by the class of compact − + plots of the parametric curve P  (), subsets of Σ of the forms J (p)∩Σ and J (p)∩Σ. Since the causal structure Z  z() for r  1 and   0, 1 and 5. determines its metric structure up to a conformal factor, this implies that the The last case corresponds to sets J−(p)∩Σ and J+(p)∩Σ determine the conformal structure of a globally vequator  0.98c. The dots show the locations of observers with   0, /6, hyperbolic spacetime. In this way, we can encode the conformal structure 2/6, . . . , . Since there is no length of the spacetime into its Cauchy surface and we get another method for contraction in a   constant plane, reconstructing spacetime. the dots are equally spaced along each curve.

A note on the nonexistence of generalized apparent horizons in Minkowski space CQG IMPACT FACTORS Marcus A Khuri CQG has seen a consistent rise in Impact Factor. 2009 Class. Quantum Grav. 26 078001 The most recent (2008) measurement shows the journal at an all-time high. We establish a positive mass theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular, we 2006 2007 2008 answer a question posed by R Wald concerning the existence of generalized 2.773* 2.846* 3.035* apparent horizons in Minkowski space. * As listed in ISI®’s 2006, 2007 and 2008 Science Citation Index Journal citation reports

22 Highlights 2009

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