Where Does the Physics of Extreme Gravitational Collapse Reside?
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What Geometries Describe Universe Near Big Bang?
Interdisciplinary Studies of Complex Systems No. 9 (2016) 5{24 c Yuri I. Manin Time Between Real and Imaginary: what Geometries Describe Universe near Big Bang? Yuri I. Manin1 Abstract. For about a century, a great challenge for theoretical physics consisted in understanding the role of quantum mode of description of our Universe (\quantum gravity"). Einstein space{times on the scale of ob- servable Universe do not easily submit to any naive quantization scheme. There are better chances to concoct a satisfying quantum picture of the very early space{time, near the Big Bang, where natural scales of events like inflation extrapolated from current observations resist any purely clas- sical description and rather require quantum input. Many physicists and mathematicians tried to understand the quantum early Universe, sometimes unaware of input of the other community. One of the goals of this article is to contribute to the communication of the two communities. In the main text, I present some ideas and results contained in the recent survey/research papers [Le13] (physicists) and [MaMar14], [MaMar15] (mathematicians). Introduction and survey 0.1. Relativistic models of space{time: Minkowski signature. Most modern mathematical models in cosmology start with description of space{time as a 4{dimensional pseudo{Riemannian manifold M endowed with metric 2 X i k ds = gikdx dx of signature (+; ; ; ) where + refers to time{like tangent vectors, whereas the infinitesimal− light{cone− − consists of null{directions. Each such manifold is a point in the infinite{dimensional configuration space of cosmological models. Basic cosmological models are constrained by Einstein equations 1 Rik Rgik + Λgik = 8πGTik − 2 and/or additional symmetry postulates, of which the most essential for us here are the so called Bianchi IX space{times, here with symmetry group SO(3), cf. -
Pulsar Scattering, Lensing and Gravity Waves
Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary Pulsar Scattering, Lensing and Gravity Waves Ue-Li Pen, Lindsay King, Latham Boyle CITA Feb 15, 2012 U. Pen Pulsar Scattering, Lensing and Gravity Waves Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary Overview I Pulsar Scattering I VLBI ISM holography, distance measures I Enhanced Pulsar Timing Array gravity waves I fuzzballs U. Pen Pulsar Scattering, Lensing and Gravity Waves Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary Pulsar Scattering I Pulsars scintillate strongly due to ISM propagation I Lens of geometric size ∼ AU I Can be imaged with VLBI (Brisken et al 2010) I Deconvolved by interstellar holography (Walker et al 2008) U. Pen Pulsar Scattering, Lensing and Gravity Waves Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary Scattering Image Data from Brisken et al, Holographic VLBI. U. Pen Pulsar Scattering, Lensing and Gravity Waves Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary ISM enigma −8 I Scattering angle observed mas, 10 rad. I Snell's law: sin(θ1)= sin(θ2) = n2=n1 −12 I n − 1 ∼ 10 . I 4 orders of magnitude mismatch. U. Pen Pulsar Scattering, Lensing and Gravity Waves Introduction Convergent Plasma Lenses Gravity Waves Black Holes/Fuzzballs Summary Possibilities I turbulent ISM: sum of many small scatters. Cannot explain discrete images. I confinement problem: super mini dark matter halos, cosmic strings? I Geometric alignment: Goldreich and Shridhar (2006) I Snell's law at grazing incidence: ∆α = (1 − n2=n1)/α I grazing incidence is geometry preferred at 2-D structures U. -
Generation of Angular Momentum in Cold Gravitational Collapse
A&A 585, A139 (2016) Astronomy DOI: 10.1051/0004-6361/201526756 & c ESO 2016 Astrophysics Generation of angular momentum in cold gravitational collapse D. Benhaiem1,M.Joyce2,3, F. Sylos Labini4,1,5, and T. Worrakitpoonpon6 1 Istituto dei Sistemi Complessi Consiglio Nazionale delle Ricerche, via dei Taurini 19, 00185 Rome, Italy e-mail: [email protected] 2 UPMC Univ. Paris 06, UMR 7585, LPNHE, 75005 Paris, France 3 CNRS IN2P3, UMR 7585, LPNHE, 75005 Paris, France 4 Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy 5 INFN Unit Rome 1, Dipartimento di Fisica, Universitá di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy 6 Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Nonthaburi Campus, 11000 Nonthaburi, Thailand Received 16 June 2015 / Accepted 4 November 2015 ABSTRACT During the violent relaxation of a self-gravitating system, a significant fraction of its mass may be ejected. If the time-varying gravi- tational field also breaks spherical symmetry, this mass can potentially carry angular momentum. Thus, starting initial configurations with zero angular momentum can, in principle, lead to a bound virialised system with non-zero angular momentum. Using numerical simulations we explore here how much angular momentum can be generated in a virialised structure in this way, starting from con- figurations of cold particles that are very close to spherically symmetric. For the initial configurations in which spherical symmetry is broken only by the Poissonian fluctuations associated with the finite particle number N, with N in range 103 to 105, we find that the relaxed structures have standard “spin” parameters λ ∼ 10−3, and decreasing slowly with N. -
Special and General Relativity with Applications to White Dwarfs, Neutron Stars and Black Holes
Norman K. Glendenning Special and General Relativity With Applications to White Dwarfs, Neutron Stars and Black Holes First Edition 42) Springer Contents Preface vii 1 Introduction 1 1.1 Compact Stars 2 1.2 Compact Stars and Relativistic Physics 5 1.3 Compact Stars and Dense-Matter Physics 6 2 Special Relativity 9 2.1 Lorentz Invariance 11 2.1.1 Lorentz transformations 11 2.1.2 Time Dilation 14 2.1.3 Covariant vectors 14 2.1.4 Energy and Momentum 16 2.1.5 Energy-momentum tensor of a perfect fluid 17 2.1.6 Light cone 18 3 General Relativity 19 3.1 Scalars, Vectors, and Tensors in Curvilinear Coordinates 20 3.1.1 Photon in a gravitational field 28 3.1.2 Tidal gravity 29 3.1.3 Curvature of spacetime 30 3.1.4 Energy conservation and curvature 30 3.2 Gravity 32 3.2.1 Einstein's Discovery 32 3.2.2 Particle Motion in an Arbitrary Gravitational Field 32 3.2.3 Mathematical definition of local Lorentz frames . 35 3.2.4 Geodesics 36 3.2.5 Comparison with Newton's gravity 38 3.3 Covariance 39 3.3.1 Principle of general covariance 39 3.3.2 Covariant differentiation 40 3.3.3 Geodesic equation from covariance principle 41 3.3.4 Covariant divergente and conserved quantities . 42 3.4 Riemann Curvature Tensor 45 x Contents 3.4.1 Second covariant derivative of scalars and vectors 45 3.4.2 Symmetries of the Riemann tensor 46 3.4.3 Test for flatness 47 3.4.4 Second covariant derivative of tensors 47 3.4.5 Bianchi identities 48 3.4.6 Einstein tensor 48 3.5 Einstein's Field Equations 50 3.6 Relativistic Stars 52 3.6.1 Metric in static isotropic spacetime 53 -
Arxiv:2010.09481V1 [Gr-Qc] 19 Oct 2020 Ally Neutral Plasma Start to Be Relevant
Radiative Penrose process: Energy Gain by a Single Radiating Charged Particle in the Ergosphere of Rotating Black Hole Martin Koloˇs, Arman Tursunov, and ZdenˇekStuchl´ık Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Bezruˇcovon´am.13,CZ-74601 Opava, Czech Republic∗ We demonstrate an extraordinary effect of energy gain by a single radiating charged particle inside the ergosphere of a Kerr black hole in presence of magnetic field. We solve numerically the covariant form of the Lorentz-Dirac equation reduced from the DeWitt-Brehme equation and analyze energy evolution of the radiating charged particle inside the ergosphere, where the energy of emitted radiation can be negative with respect to a distant observer in dependence on the relative orientation of the magnetic field, black hole spin and the direction of the charged particle motion. Consequently, the charged particle can leave the ergosphere with energy greater than initial in expense of black hole's rotational energy. In contrast to the original Penrose process and its various modification, the new process does not require the interactions (collisions or decay) with other particles and consequent restrictions on the relative velocities between fragments. We show that such a Radiative Penrose effect is potentially observable and discuss its possible relevance in formation of relativistic jets and in similar high-energy astrophysical settings. INTRODUCTION KERR SPACETIME AND EXTERNAL MAGNETIC FIELD The fundamental role of combined strong gravitational The Kerr metric in the Boyer{Lindquist coordinates and magnetic fields for processes around BH has been and geometric units (G = 1 = c) reads proposed in [1, 2]. -
A Conceptual Model for the Origin of the Cutoff Parameter in Exotic Compact Objects
S S symmetry Article A Conceptual Model for the Origin of the Cutoff Parameter in Exotic Compact Objects Wilson Alexander Rojas Castillo 1 and Jose Robel Arenas Salazar 2,* 1 Departamento de Física, Universidad Nacional de Colombia, Bogotá UN.11001, Colombia; [email protected] 2 Observatorio Astronómico Nacional, Universidad Nacional de Colombia, Bogotá UN.11001, Colombia * Correspondence: [email protected] Received: 30 October 2020; Accepted: 30 November 2020 ; Published: 14 December 2020 Abstract: A Black Hole (BH) is a spacetime region with a horizon and where geodesics converge to a singularity. At such a point, the gravitational field equations fail. As an alternative to the problem of the singularity arises the existence of Exotic Compact Objects (ECOs) that prevent the problem of the singularity through a transition phase of matter once it has crossed the horizon. ECOs are characterized by a closeness parameter or cutoff, e, which measures the degree of compactness of the object. This parameter is established as the difference between the radius of the ECO’s surface and the gravitational radius. Thus, different values of e correspond to different types of ECOs. If e is very big, the ECO behaves more like a star than a black hole. On the contrary, if e tends to a very small value, the ECO behaves like a black hole. It is considered a conceptual model of the origin of the cutoff for ECOs, when a dust shell contracts gravitationally from an initial position to near the Schwarzschild radius. This allowed us to find that the cutoff makes two types of contributions: a classical one governed by General Relativity and one of a quantum nature, if the ECO is very close to the horizon, when estimating that the maximum entropy is contained within the material that composes the shell. -
Stellar Equilibrium Vs. Gravitational Collapse
Eur. Phys. J. H https://doi.org/10.1140/epjh/e2019-100045-x THE EUROPEAN PHYSICAL JOURNAL H Stellar equilibrium vs. gravitational collapse Carla Rodrigues Almeidaa Department I Max Planck Institute for the History of Science, Boltzmannstraße 22, 14195 Berlin, Germany Received 26 September 2019 / Received in final form 12 December 2019 Published online 11 February 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com Abstract. The idea of gravitational collapse can be traced back to the first solution of Einstein's equations, but in these early stages, com- pelling evidence to support this idea was lacking. Furthermore, there were many theoretical gaps underlying the conviction that a star could not contract beyond its critical radius. The philosophical views of the early 20th century, especially those of Sir Arthur S. Eddington, imposed equilibrium as an almost unquestionable condition on theoretical mod- els describing stars. This paper is a historical and epistemological account of the theoretical defiance of this equilibrium hypothesis, with a novel reassessment of J.R. Oppenheimer's work on astrophysics. 1 Introduction Gravitationally collapsed objects are the conceptual precursor to black holes, and their history sheds light on how such a counter-intuitive idea was accepted long before there was any concrete proof of their existence. A black hole is a strong field structure of space-time surrounded by a unidirectional membrane that encloses a singularity. General relativity (GR) predicts that massive enough bodies will collapse into black holes. In fact, the first solution of Einstein's field equations implies the existence of black holes, but this conclusion was not reached at the time because the necessary logical steps were not as straightforward as they appear today. -
Collapse of an Unstable Neutron Star to a Black Hole Matthias Hanauske (E-Mail:[email protected], Office: 02.232)
Experiments in Computer Simulations : Collapse of an unstable Neutron Star to a Black Hole Matthias Hanauske (e-mail:[email protected], office: 02.232) 0 Class Information • application form : { if you want to do this experiment, please register via e-mail to me no later than on the last Wednesday before the week in which you want to do the experiment; your e-mail should include the following information: (1) student number, (2) full name, (3) e-mail address. • intensive course : { 12 [hours] = 6 [hours/week] × 2 [weeks]. • when : { Monday 9-16, two subsequent weeks upon individual arrangement with me; other time slots may be arranged with me individually. • where : { Pool Room 01.120. • preparation : { an account for you on the \FUCHS" cluster of the CSC (http://csc.uni-frankfurt.de/) will be provided; please read the quick starting guide on the CSC web pages before starting the simulation. • required skill : { basic Linux knowledge. • using software : { Einstein Toolkit [5]. { gnuplot (http://www.gnuplot.info/) { pygraph (https://bitbucket.org/dradice/pygraph). { python (https://www.python.org/) and matplotlib (http://matplotlib.org/). { Mathematica (http://www.wolfram.com/mathematica/). 1 1 Introduction Neutron stars are beside white dwarfs and black holes the potential final states of the evo- lution of a normal star. These extremely dense astrophysical objects, which are formed in the center of a supernova explosion, represent the last stable state before the matter collapses to a black hole. Due to their large magnetic fields (up to 1011 Tesla) and fast rotation (up to 640 rotations in one second) neutron stars emit a certain electromagnetic spectrum. -
Energetics of the Kerr-Newman Black Hole by the Penrose Process
J. Astrophys. Astr. (1985) 6, 85 –100 Energetics of the Kerr-Newman Black Hole by the Penrose Process Manjiri Bhat, Sanjeev Dhurandhar & Naresh Dadhich Department of Mathematics, University of Poona, Pune 411 007 Received 1984 September 20; accepted 1985 January 10 Abstract. We have studied in detail the energetics of Kerr–Newman black hole by the Penrose process using charged particles. It turns out that the presence of electromagnetic field offers very favourable conditions for energy extraction by allowing for a region with enlarged negative energy states much beyond r = 2M, and higher negative values for energy. However, when uncharged particles are involved, the efficiency of the process (defined as the gain in energy/input energy) gets reduced by the presence of charge on the black hole in comparison with the maximum efficiency limit of 20.7 per cent for the Kerr black hole. This fact is overwhelmingly compensated when charged particles are involved as there exists virtually no upper bound on the efficiency. A specific example of over 100 per cent efficiency is given. Key words: black hole energetics—Kerr-Newman black hole—Penrose process—energy extraction 1. Introduction The problem of powering active galactic nuclei, X-raybinaries and quasars is one of the most important problems today in high energy astrophysics. Several mechanisms have been proposed by various authors (Abramowicz, Calvani & Nobili 1983; Rees et al., 1982; Koztowski, Jaroszynski & Abramowicz 1978; Shakura & Sunyaev 1973; for an excellent review see Pringle 1981). Rees et al. (1982) argue that the electromagnetic extraction of black hole’s rotational energy can be achieved by appropriately putting charged particles in negative energy orbits. -
Schwarzschild Black Hole Can Also Produce Super-Radiation Phenomena
Schwarzschild black hole can also produce super-radiation phenomena Wen-Xiang Chen∗ Department of Astronomy, School of Physics and Materials Science, GuangZhou University According to traditional theory, the Schwarzschild black hole does not produce super radiation. If the boundary conditions are set in advance, the possibility is combined with the wave function of the coupling of the boson in the Schwarzschild black hole, and the mass of the incident boson acts as a mirror, so even if the Schwarzschild black hole can also produce super-radiation phenomena. Keywords: Schwarzschild black hole, superradiance, Wronskian determinant I. INTRODUCTION In a closely related study in 1962, Roger Penrose proposed a theory that by using point particles, it is possible to extract rotational energy from black holes. The Penrose process describes the fact that the Kerr black hole energy layer region may have negative energy relative to the observer outside the horizon. When a particle falls into the energy layer region, such a process may occur: the particle from the black hole To escape, its energy is greater than the initial state. It can also show that in Reissner-Nordstrom (charged, static) and rotating black holes, a generalized ergoregion and similar energy extraction process is possible. The Penrose process is a process inferred by Roger Penrose that can extract energy from a rotating black hole. Because the rotating energy is at the position of the black hole, not in the event horizon, but in the area called the energy layer in Kerr space-time, where the particles must be like a propelling locomotive, rotating with space-time, so it is possible to extract energy . -
One Or Several Populations of Fast Radio Burst Sources?
One or several populations of fast radio burst sources? M. Caleb1, L. G. Spitler2 & B. W. Stappers1 1Jodrell Bank Centre for Astrophysics, the University of Manchester, Manchester, UK. 2Max-Planck-Institut fu¨r Radioastronomie, Bonn, Germany. arXiv:1811.00360v1 [astro-ph.HE] 1 Nov 2018 1 To date, one repeating and many apparently non-repeating fast radio bursts have been de- tected. This dichotomy has driven discussions about whether fast radio bursts stem from a single population of sources or two or more different populations. Here we present the arguments for and against. The field of fast radio bursts (FRBs) has increasingly gained momentum over the last decade. Overall, the FRBs discovered to date show a remarkable diversity of observed properties (see ref 1, http://frbcat.org and Fig. 1). Intrinsic properties that tell us something about the source itself, such as polarization and burst profile shape, as well as extrinsic properties that tell us something about the source’s environment, such as the magnitude of Faraday rotation and multi-path propagation effects, do not yet present a coherent picture. Perhaps the most striking difference is between FRB 121102, the sole repeating FRB2, and the more than 60 FRBs that have so far not been seen to repeat. The observed dichotomy suggests that we should consider the existence of multiple source populations, but it does not yet require it. Most FRBs to date have been discovered with single-pixel telescopes with relatively large angular resolutions. As a result, the non-repeating FRBs have typically been localized to no bet- ter than a few to tens of arcminutes on the sky (Fig. -
Planck Stars: New Sources in Radio and Gamma Astronomy? Nature Astronomy 1 (2017) 0065
Planck stars: new sources in radio and gamma astronomy? Nature Astronomy 1 (2017) 0065 Carlo Rovelli CPT, Aix-Marseille Universit´e,Universit´ede Toulon, CNRS, F-13288 Marseille, France. A new phenomenon, recently studied in theoretical ble according to classical general relativity, but there is physics, may have considerable interest for astronomers: theoretical consensus that they decay via quantum pro- the explosive decay of old primordial black holes via cesses. Until recently, the only decay channel studied was quantum tunnelling. Models predict radio and gamma Hawking evaporation [6], a perturbative phenomenon too bursts with a characteristic frequency-distance relation slow to have astrophysical interest: evaporation time of making them identifiable. Their detection would be of a stellar black hole is 1050 Hubble times. major theoretical importance. What can bring black hole decay within potential ob- The expected signal may include two components [1]: servable reach is a different, non-perturbative, quantum (i) strong impulsive emission in the high-energy gamma phenomenon: tunnelling, the same phenomenon that spectrum (∼ T eV ), and (ii) strong impulsive signals triggers nuclear decay in atoms. The explosion of a black in the radio, tantalisingly similar to the recently dis- hole out of its horizon is forbidden by the classical Ein- covered and \very perplexing" [2] Fast Radio Bursts. stein equations but classical equations are violated by Both the gamma and the radio components are expected quantum tunnelling. Violation in a finite spacetime re- to display a characteristic flattening of the cosmological gion turns out to be sufficient for a black hole to tun- wavelength-distance relation, which can make them iden- nel into a white hole and explode [7].