DOCSLIB.ORG

Quantum of the Gravitational Field. Theoretical and Experimental Substantiation of Gravitational Electromagnetic Resonance

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum of the Gravitational Field. Theoretical and Experimental Substantiation of Gravitational Electromagnetic Resonance Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.. 2020. hal-02553557 HAL Id: hal-02553557 https://hal.archives-ouvertes.fr/hal-02553557 Preprint submitted on 24 Apr 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UDC 001.5:53.02:53.05 Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine 2Research and Production Enterprise «TZHK», Researcher, Ukraine *Email: [email protected] Annotation. It is shown that gravitating objects that are at rest, or move without acceleration, create a standing gravitational wave in space. The length of this wave is a quantization step of the gravitational field. It is proportional to the mass of the gravitating object. The coefficient of proportionality is a value that is inverse to the linear density of the Planck mass, that is, proportional to the linear rarefaction of the Planck mass. A physically standing gravitational wave is a curvature, deformation of space under the influence of the gravitational field of a gravitating object. If we imagine a gravitating object as a material point, then the geometric picture of a standing gravitational wave can be represented as a set of hierarchical spherical equipotential surfaces embedded in each other, the radius of which changes away from the center of gravity by the value of the quantization step. It is shown that a standing gravitational wave has a quantum character. The quantum of the gravitational field is the square of the speed of light in a vacuum. The quantum of the gravitational field is equal to the gravitational potential of the gravitating object at a distance from it equal to the quantization step. Theoretical and experimental substantiation of the presence of gravitational-electromagnetic resonance (GER) in nature is given. This resonance arises when the wave vectors of a standing gravitational wave and an electromagnetic wave traveling in space are equal. GER is the basis for modulating the emission spectrum of stars and their clusters. The wavelength of the envelope of the spectrum is proportional to the mass of the radiating object. By measuring the wavelength of the envelope, one can accurately estimate the mass of the radiating object. Keywords: Maxwell-like equations of the gravitational field, the standing gravitational wave, the quantum of the gravitational field, the gravitational electromagnetic resonance, Planck constants. Introduction. The gravitational field has a wave character [1,2]. There are two types of gravitational waves: a gravitational wave traveling in space [3,4,5], which depends on time, and a standing gravitational wave [6,7,8], which does not depend on time. In both cases, the gravitational wave is a deformation of space, a change in its curvature under the influence of the mass of the gravitating body. A prerequisite for the existence of a gravitational wave traveling in space is a movement with the acceleration of massive objects [3]. This movement generates a wave-like change in the curvature of space-time, which propagates from accelerating objects with the speed of light in a vacuum in the form of traveling gravitational waves. A real source of gravitational waves traveling in space can be, for example, two black holes merging into one, which rotates around each other. Each of the black holes moving with acceleration emits traveling gravitational waves, but according to Newton’s third law, the forces with which they act on each other are balanced, therefore, as a result of the interference formed, these traveling gravitational waves are almost completely mutually quenched. According to the general theory of relativity, the source of traveling gravitational waves from merging black holes is the quadrupole moment of their accelerating composite mass [3,9], which is called chirp mass. A standing gravitational wave is a deformation, a curvature of the space around a gravitating object, which is represented as a set of fractal spherical equipotential surfaces embedded in each other with a common center that coincides with the center of mass of this object. The radius of the spheres varies with a step that is proportional to the mass of the gravitating object [6]. This step is called the length of the standing gravitational wave. A standing gravitational wave can be a modulation source of a traveling gravitational wave. Under certain conditions, a standing gravitational wave can be a source of gravitational-electromagnetic resonance. A prerequisite for this is the fact that the electromagnetic field is a special case of the gravitational field [10]. The technological condition for the existence of gravitational electromagnetic resonance is the equality of the wave vectors (wavenumbers) of the standing gravitational wave and the traveling (standing) electromagnetic wave. A standing gravitational field is quantized in space. The quantum of the gravitational field is the square of the speed of light in a vacuum. The quantum of the gravitational field is equal to the gravitational potential of the gravitating object at a distance from it equal to the quantization step. Maxwell-like equations of the gravitational field. Let a charged test particle, the charge and mass of which q and m respectively, are simultaneously in the electromagnetic and gravitational fields, then from the side of these fields on the test particle the forces act: electromagnetic Fe , gravitational Fg : Fe = q ( E + V B ), Fg= m ( E g + V k B g ), (1) where E is the vector of electric field strength, V is the velocity vector of the test particle, B is the vector of the magnetic induction of the magnetic field, () is the sign of the vector product, Eg is the vector of the gravitational field strength, Bg is the gravitomagnetic induction flux vector, k is the dimensionless correction coefficient which equals 1 in the Heaviside equations and 2 or 4 in the equations based on the general theory of relativity. Obviously, the dimension of the vector Eg in the formula (1) - has the dimension of acceleration and the dimension of vector Bg - of frequency. The Coulomb law for two charges q1 and q2 at a distance of r12 from each other and the law of gravity for two bodies, whose masses are m1 and m2 , and which are at a distance of from each other, have the form: q1 q 2 r 12 m1 m 2 r 12 FkeE= , FGg = , (2) rr12 12 rr12 12 where: kE is the proportionality factor (Coulomb's constant, or the electric force constant ), r12 is radius-vector, G is a gravitational constant. An analysis of equations (1,2) shows that the structures of the gravitational and electromagnetic fields are similar. Accordingly, the equations that describe these fields should be similar. The electromagnetic field is described by the Maxwell equations. Based on them, Heaviside [1] proposed a description of the gravitational field. These equations are called Maxwell-like Heaviside equations, or they are also called gravitoelectromagnetic equations. To form a description of the gravitational field in the form of gravitoelectromagnetic equations, we consider the Maxwell equations [11]: E = , (3) 0 B = 0, (4) B H E = − = − 0 , (5) tt 11E BJ =22 + , (6) 0c c t where: c is the speed of light in vacuum, is the charge density, 0 is the vacuum permittivity, 0 is the magnetic constant, H is the vector of the magnetic field strength, J is the electric current density. Based on Maxwell's equations (3,4,5,6) we obtain the wave equations of the electromagnetic field. To do this, vectorially multiply by the operator nabla the left and right sides of equation (5), we obtain: HDE 22 =−EHE =− =− =− =− , (7) 0 0( ) 0 022( 0) 0 0 t t t t t t where D is the electric displacement vector. Given that: 1 = , (8) 00 c2 EEE =( ) −2 , (9) we get: 2 2 1 E ( EE) − = − 22. (10) ct Since the divergence of the electric displacement vector in a dielectric medium satisfies the condition: D = 0, (11) then the divergence of the electric field vector in a homogeneous medium (for example, vacuum) satisfies the condition: E = 0, (12) then equation (10) takes the form: 1 2 E 2 E = − . (13) ct22 Vector equation (13) can be represented in the form of three scalar equations: 22 EExx1 2=− 2 2 x c t 22 EEyy1 2=− 2 2 (14) y c t 22EE1 zz=− . z2 c 2 t 2 Similarly, we can obtain the wave equation for the magnetic component H of the electromagnetic field: 2 2 1 H H = − 22, (15) ct 22 HHxx1 2=− 2 2 x c t 22 HHyy1 2=− 2 2 (16) y c t 22HH1 zz=− . z2 c 2 t 2 Equations (13) and (15) are homogeneous wave equations. Each scalar function in equations (14,16) of the projections of vectors E and H can be represented as a generalized function V , then we come to the Poisson equation: 1 2V 2V = − .
Load more

Recommended publications
  • Page Curve for an Evaporating Black Hole Arxiv:2004.00598V2 [Hep-Th]
    Page Curve for an Evaporating Black Hole Friðrik Freyr Gautason?, Lukas Schneiderbauer?, Watse Sybesma? and Lárus Thorlacius? Instituut voor Theoretische Fysica, KU Leuven Celestijnenlaan 200D, 3001 Leuven, Belgium ?Science Institute University of Iceland Dunhaga 3, 107 Reykjavík, Iceland. E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: A Page curve for an evaporating black hole in asymptotically flat spacetime is computed by adapting the Quantum Ryu-Takayanagi (QRT) proposal to an analytically solvable semi-classical two-dimensional dilaton gravity theory. The Page time is found to be one third of the black hole lifetime, at leading order in semi- classical corrections. A Page curve is also obtained for a semi-classical eternal black hole, where energy loss due to Hawking evaporation is balanced by an incoming energy flux. arXiv:2004.00598v2 [hep-th] 21 Apr 2020 Contents 1 Introduction1 2 Page curve from QRT3 3 The model6 3.1 Coupling to matter7 3.2 Semi-classical black holes9 4 Generalized entropy 12 5 Page curves 13 5.1 Eternal black hole 13 5.2 Dynamical black hole 17 5.2.1 Island configuration 17 5.2.2 No-island configuration 20 6 Discussion 20 1 Introduction If black hole evaporation is a unitary process, the entanglement entropy between the outgoing radiation and the quantum state associated to the remaining black hole is expected to follow the so-called Page curve as a function of time [1,2]. Early on, the entanglement entropy is then a monotonically increasing function of time which closely tracks the coarse grained thermal entropy of the radiation that has been emitted up to that point.
    [Show full text]
  • A New Look at the RST Model Jian-Ge Zhoua, F. Zimmerschieda, J
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server A new lo ok at the RST mo del a a a,b Jian-Ge Zhou , F. Zimmerschied , J.{Q. Liang and a H. J. W. Muller{Ki rsten a Department of Physics, University of Kaiserslautern, P. O. Box 3049, D{67653 Kaiserslautern, Germany b Institute of Theoretical Physics, Shanxi University Taiyuan, Shanxi 030006, P. R. China and Institute of Physics, Academia Sinica, Beijing 100080, P. R. China Abstract The RST mo del is augmented by the addition of a scalar eld and a b oundary term so that it is well-p osed and lo cal. Expressing the RST action in terms of the ADM formulation, the constraint structure can b e analysed completely.It is shown that from the view p oint of lo cal eld theories, there exists a hidden dynamical eld in the RST mo del. Thanks to the presence of this hidden 1 dynamical eld, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors T are recovered to b e true tensor quantities. Esp ecially, the part of the stress tensors for the hidden dynamical eld gives the precise expression for t . 1 At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical eld , the fact 1 that the semi-classical static solution of the RST mo del has two indep endent parameters (P,M), whereas for the classical CGHS mo del there is only one, can b e explained.
    [Show full text]
  • In#Ationary Cosmology
    PLREP 984 BALA EM yamuna Physics Reports 333}334 (2000) 575}591 In#ationary cosmology Andrei Linde Department of Physics, Stanford University, Stanford, CA 94305-4060, USA Abstract The evolution of the in#ationary theory is described, starting from the Starobinsky model and the old in#ation scenario, toward chaotic in#ation and the theory of eternally expanding self-reproducing in#ation- ary universe. I discuss also the recent development of in#ationary models with XO1 and the progress in the theory of reheating after in#ation. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 98.80.Cq Keywords: In#ation; Cosmology; Global structure; Preheating 1. Introduction In#ationary theory was proposed 20 years ago. In the beginning it looked like an interesting piece of science "ction. During the last 20 years it changed quite a lot and became a broadly accepted cosmological paradigm. New versions of this theory do not require any assumptions about initial thermal equilibrium in the early universe. In#ation is no longer based on the mechanism of supercooling and exponential expansion in the false vacuum state. It was proposed in order to resolve various problems of the big bang theory, and in particular to explain the extraordinary homogeneity of the observable part of the universe. However, later we have learned that while making the universe locally homogeneous, in#ation can make it extremely in- homogeneous on a very large scale. According to the simplest versions of in#ationary theory the universe is not a single, expanding ball of "re produced in the big bang, but rather a huge eternally growing fractal.
    [Show full text]
  • Conformal Anomaly for 2D and 4D Dilaton Coupled Spinors
    NDA-FP-55 January 1999 Conformal anomaly for 2d and 4d dilaton coupled spinors Peter van Nieuwenhuizen1 2 3 Shin’ichi Nojiri♣ and Sergei D. Odintsov♠ Institute for Theoretical Physics State University of New York Stony Brook, NY 11794-3840, USA Department of Mathematics and Physics ♣ National Defence Academy Hashirimizu Yokosuka 239, JAPAN Tomsk Pedagogical University ♠ 634041 Tomsk, RUSSIA ABSTRACT We study quantum dilaton coupled spinors in two and four dimensions. Making classical transformation of metric, dilaton coupled spinor theory is transformed to minimal spinor theory with another metric and in case of 4d spinor also in the background of the non-trivial vector field. This gives the possibility to calculate 2d and 4d dilaton dependent conformal (or Weyl) anomaly in easy way. Anomaly induced effective action for such spinors is de- rived. In case of 2d, the effective action reproduces, without any extra terms, arXiv:hep-th/9901119v1 25 Jan 1999 the term added by hands in the quantum correction for RST model, which is exactly solvable. For 4d spinor the chiral anomaly which depends explic- itly from dilaton is also found. As some application we discuss SUSY Black Holes in dilatonic supergravity with WZ type matter and Hawking radiation in the same theory. As another application we investigate spherically reduced Einstein gravity with 2d dilaton coupled fermion anomaly induced effective action and show the existence of quantum corrected Schwarszchild-de Sitter (SdS) (Nariai) BH with multiple horizon. 1 e-mail : [email protected] 2 e-mail : [email protected] 3 e-mail : [email protected] 1 1 Introduction Spherical reduction of Einstein gravity (see, for example [1]) with minimal matter leads to some 2d dilatonic gravity (for most general action, see [2]) with 2d dilaton coupled matter.
    [Show full text]
  • Semi-Classical Black Hole Holography
    Dissertation for the degree of Doctor of Philosophy Semi-Classical Black Hole Holography Lukas Schneiderbauer School of Engineering and Natural Sciences Faculty of Physical Sciences Reykjavík, September 2020 A dissertation presented to the University of Iceland, School of Engineering and Natural Sciences, in candidacy for the degree of Doctor of Philosophy. Doctoral committee Prof. Lárus Thorlacius, advisor Faculty of Physical Sciences, University of Iceland Prof. Þórður Jónsson Faculty of Physical Sciences, University of Iceland Prof. Valentina Giangreco M. Puletti Faculty of Physical Sciences, University of Iceland Prof. Bo Sundborg Department of Physics, Stockholm University Opponents Prof. Veronika Hubeny University of California, Davis Prof. Mukund Rangamani University of California, Davis Semi-classical Black Hole Holography Copyright © 2020 Lukas Schneiderbauer. ISBN: 978-9935-9452-9-7 Author ORCID: 0000-0002-0975-6803 Printed in Iceland by Háskólaprent, Reykjavík, Iceland, September 2020. Contents Abstractv Ágrip (in Icelandic) vii Acknowledgementsx 1 Introduction1 2 Black Hole Model7 2.1 The Polyakov term . .8 2.2 The stress tensor . 11 2.3 Coherent matter states . 14 2.4 The RST term . 15 2.5 Equations of motion . 15 2.6 Black hole thermodynamics . 17 3 Page Curve 21 3.1 Generalized entropy . 24 4 Quantum Complexity 27 4.1 Complexity of black holes . 29 4.2 The geometric dual of complexity . 32 5 Conclusion 35 Bibliography 37 Articles 47 Article I ..................................... 49 iii Article II .................................... 67 Article III .................................... 99 iv Abstract This thesis discusses two aspects of semi-classical black holes. First, a recently improved semi-classical formula for the entanglement entropy of black hole radiation is examined.
    [Show full text]
  • Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics
    Fundamental Theories of Physics 178 Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics Volume 178 Series editors Henk van Beijeren Philippe Blanchard Paul Busch Bob Coecke Dennis Dieks Detlef Dürr Roman Frigg Christopher Fuchs Giancarlo Ghirardi Domenico J.W. Giulini Gregg Jaeger Claus Kiefer Nicolaas P. Landsman Christian Maes Hermann Nicolai Vesselin Petkov Alwyn van der Merwe Rainer Verch R.F. Werner Christian Wuthrich More information about this series at http://www.springer.com/series/6001 Xavier Calmet Editor Quantum Aspects of Black Holes 123 Editor Xavier Calmet Department of Physics and Astronomy University of Sussex Brighton UK ISBN 978-3-319-10851-3 ISBN 978-3-319-10852-0 (eBook) DOI 10.1007/978-3-319-10852-0 Library of Congress Control Number: 2014951685 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
    [Show full text]
  • Entropy in the RST Model
    DAMTP-R94/61 Phys. Rev D52.4 (1995) Entropy in the RST Model Justin D. Hayward1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K. December 1994 Abstract The RST Model is given boundary term and Z-field so that it is well-posed and local. The Euclidean method is described for general theory and used to cal- culate the RST intrinsic entropy. The evolution of this entropy for the shockwave solutions is found and obeys a second law. arXiv:gr-qc/9412065v2 3 Aug 1995 1E-mail address: [email protected] 1 Introduction A notable development in the ongoing study of the black hole evaporation problem[1] is that there is now a two dimensional model which admits physically sensible evaporating black hole solutions [2], at least for much of the process. In[3], it was shown that if the radiation in the scalar degrees of freedom which produce a black-hole like object, has positive energy, there must be a global event horizon or a naked singularity. This was a general argument which did not depend upon the precise fine-tuning of the model: only the general form of the global structure was determined. If a spacetime has a global event horizon or a naked singularity, one can say through reasonable qualitative statements that the former case implies loss of quantum coherence, while the latter would lead to an even worse breakdown of predictability. Whilst such qualitative arguments are convincing, at least at the semi-classical level, (a consideration of superselection sectors in a third quantised framework[4] may lead to other possibilities), one would like to prepare explicit calculations which show that some physical quantity changes during the evolution of a spacetime in such a way that it is clearly seen whether there is loss of information.
    [Show full text]
  • Dark Matter Model of the Universe”, Physics Essays, V25, N0
    Jerry Hynecek © 2014, Isetex, Inc. 4/4/2014 © 2014, Isetex, Inc. 1 An interesting journey of discovery This is a concise slide presentation of my foray into the Special and General Relativity Theories. Abstract: The presentation deals with a discovery of errors in the Einstein’s General Relativity Theory (GRT). The presentation starts with the confirmation of the correctness of Special Relativity Theory (SRT), but derives justification for a different dependence of gravitational mass on velocity than the inertial mass dependence on velocity. This leads to finding that photons cannot have a gravitational mass and thus can escape form “Black Holes”. This finding contradicts the popular belief and the popular statements such as: “not even light can escape from Black Holes”. The presentation then introduces a new metric whose validity has been confirmed by the standard GRT tests and applies it to create a new model of the universe, which is not based on the Big Bang assumption. Finally, the new universe model predictions are compared with observations and an excellent agreement is obtained thus confirming the assumptions on which the model is built. 4/4/2014 © 2014, Isetex, Inc. 2 Presentation outline Introduction: the message from the ghost of Einstein Special Relativity Theory: the mass equivalence as a first hint of a problem The new metric for spacetime The test of light trajectory bending by gravity Motivation for modeling the universe Turning BB theory on its head Hubble telescope dates oldest star, 'Methuselah', at 14.5 billion years old The new universe model assumptions Supporting mathematical background Comparison with observations Hubble diagram Accelerating universe? More comparisons with observations Quantum of the repulsive Dark Matter Possible evidence for gravitational waves Conclusions Summary of some fundamental principles Closing remarks Recent claims and revisions of the BB theory Interesting similarities between various theories Links to posted papers related to this work Reference literature 4/4/2014 © 2014, Isetex, Inc.
    [Show full text]
  • Stability of Black Holes in Two-Dimensional Dilaton Gravity (*)
    IL NUOVO CIMENTOVOL. 112 B, N. 12 Dicembre 1997 Stability of black holes in two-dimensional dilaton gravity (*) M. A. AHMED Physics Department, Kuwait University - Kuwait (ricevuto il 14 Aprile 1997; approvato il 3 Giugno 1997) Summary. — We discuss the stability of black-hole solutions in a model of two-dimensional dilaton gravity. We show that the black hole is stable under small nonstatic perturbations. PACS 04.70.Dy – Quantum aspects of black holes, evaporation, thermodynamics. PACS 04.60.Kz – Lower dimensional models; minisuperspace models. 1. – Introduction In recent years there has been a lot of interest in the string-inspired gravity theories in two space-time dimensions [1, 2]. In particular, in ref. [3] Callan et al. (CGHS) included matter fields and discussed the phenomenon of Hawking radiation. A solution in closed form for the quantum corrected CGHS equations had not been found. This led Russo et al. [4] (RST) to present a modification of the CGHS model by adding a term of the form fR to the action, with f being the dilaton field and R the scalar curvature. This form appears in the RST model with a coefficient equal to N/12, where N is the number of matter fields. By performing certain field redefinitions, RST were able to solve the field equations following from the model exactly. In ref. [5] we considered a generalization of the dilaton gravity model by allowing the fR term to enter with an arbitrary coefficient and we were able to solve the resulting field equations exactly. Once one has an exact solution, to investigate its stability becomes an interesting issue.
    [Show full text]
  • JHEP07(2020)022.Pdf
    Published for SISSA by Springer Received: May 28, 2020 Accepted: June 15, 2020 Published: July 3, 2020 Islands in asymptotically flat 2D gravity JHEP07(2020)022 Thomas Hartman,a Edgar Shaghouliana and Andrew Stromingerb aDepartment of Physics, Cornell University, Ithaca, New York, U.S.A. bDepartment of Physics, Harvard University, Cambridge, MA, U.S.A. E-mail: [email protected], [email protected], [email protected] Abstract: The large-N limit of asymptotically flat two-dimensional dilaton gravity cou- pled to N free matter fields provides a useful toy model for semiclassical black holes and the information paradox. Analyses of the asymptotic information flux as given by the entanglement entropy show that it follows the Hawking curve, indicating that information is destroyed in these models. Recently, motivated by developments in AdS/CFT, a semi- classical island rule for entropy has been proposed. We define and compute the island rule entropy for black hole formation and evaporation in the large-N RST model of dilaton gravity and show that, in contrast, it follows the unitary Page curve. The relation of these two observations, and interesting properties of the dilaton gravity island rule, are discussed. Keywords: 2D Gravity, Black Holes, Models of Quantum Gravity ArXiv ePrint: 2004.13857 Open Access, c The Authors. https://doi.org/10.1007/JHEP07(2020)022 Article funded by SCOAP3. Contents 1 Introduction1 2 Review of the RST model4 2.1 Large-N action and equation of motion4 2.2 Solutions6 2.2.1 Linear dilaton vacuum6 JHEP07(2020)022
    [Show full text]
  • Black Holes Entropy and the Semiclassical Approximation
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server hep-th/9404135 BLACK HOLES ENTROPY AND THE SEMICLASSICAL APPROXIMATION SAMIR D. MATHUR Center for Theoretical Physics Massachussetts Institute of Technology, Cambridge, MA 02139, USA ABSTRACT We compute the entropy of the Hawking radiation for an evap orating black hole, in 1+1 dimensions and in 3+1 dimensions. We give a cri- terion for semiclassicality of the evap oration pro cess. It app ears that there might b e a large entropyofentanglementbetween the infalling matter and the radiation when quantum gravity is considered. Invited talk given at the International Collo quium on Mo dern Quantum Field Theory I I at TIFR (Bombay) January 1994. 1. Intro duction Recently there has b een a renewed interest in the black hole evap oration prob- lem, and the asso ciated problem of information loss. One reason is the construction 1;2 of 1+1 dimensional mo dels where evap orating holes can b e easily studied . An- 3 other reason is a spate of work on the prop osal of 't Ho oft that the black hole evap oration pro cess may not b e semiclassical. This idea is based on the fact that + 1 although the Hawking radiation at I is low frequency ( M ) it originates in very M high frequency vacuum mo des at I , the latter frequency b eing e times the planck frequency.(Mis the mass of the black hole in planck units.) The need to consider sup er-planckian frequencies suggests that the black hole evap oration pro cess involves quantum gravity, and cannot b e approximated bya semiclassical calculation of ` eld theory on curved space'.
    [Show full text]
  • Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole
    Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole Lukas Schneiderbauer, Watse Sybesma and L´arusThorlacius Science Institute, University of Iceland, Dunhaga 3, 107 Reykjav´ık,Iceland. E-mail: [email protected], [email protected], [email protected] Abstract: We obtain the holographic complexity of an evaporating black hole in the semi-classical RST model of two-dimensional dilaton gravity, using a volume prescription that takes into account the higher-dimensional origin of the model. For classical black holes, we recover the expected late time behaviour of the complexity, but new features arise at the semi-classical level. By considering the volume inside the stretched horizon of the evolving black hole, we obtain sensible results for the rate of growth of the complexity, with an early onset of order the black hole scrambling time followed by an extended period where the rate of growth tracks the shrinking area of the stretched horizon as the black hole evaporates. arXiv:1911.06800v2 [hep-th] 3 Apr 2020 Contents 1 Introduction1 2 Complexity of classical CGHS black holes2 2.1 Complexity of a two-sided black hole3 2.2 Complexity of a black hole formed by gravitational collapse7 3 The RST model: Complexity in a semi-classical black hole9 4 Conclusion and outlook 12 1 Introduction The interior of a black hole is the archetype of an emergent spacetime in the holographic approach to quantum gravity. The principle of black hole complementarity posits that the interior geometry and any matter that enters a black hole can be described in terms of a finite number of quantum mechanical degrees of freedom associated with a stretched horizon located outside the event horizon [1].
    [Show full text]