Chapters of Advanced General Relativity
|
|
- Adrian Lane
- 6 years ago
- Views:
Transcription
1 Chapters of Advanced General Relativity Notes for the Amsterdam-Brussels-Geneva-Paris doctoral school 2014 & 2016 In preparation Glenn Barnich Physique Théorique et Mathématique Université Libre de Bruxelles and International Solvay Institutes Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium Abstract. The major aim of the course is to provide technical background material needed for standard computations in general relativity and its extensions. The material covered includes the Cartan formulation, variational principles of gravitational theories, the Newman-Penrose formalism and theoretical aspects of black hole physics. The choice of chapters is to a large extent idiosyncratic.
2 Contents 1 Elements of differential geometry Manifolds and functions Tangent vectors and vector fields Covectors Tensor algebra Metrics Differential forms Maps and Lie derivative Affine connection and covariant derivative Matter couplings Variations Exercices Variational principles for Einstein s equations Auxiliary fields and symmetries Gauge symmetries Metric formulation Palatini formulation Cartan formulation Einstein-Dirac theory d gravity as a Chern-Simons theory Newman-Penrose formalism Null basis and spin coefficients Weyl, Ricci and Riemann tensor Structure constants Bianchi identities Lorentz transformations and gauge fixation Optical scalars Petrov classification Goldberg-Sachs theorem Black holes Killing horizons Schwarzschild black hole and Rindler spacetime Kerr black hole The first law of black hole mechanics
3 5 Asymptotics Asymptotic symmetries Acknowledgements 9 References 9
4 1 Elements of differential geometry This section mostly follows [1]. Other references I have found useful are [2], [3], [4]. Missing proofs of Frobenius and Stokes theorem can be found in [5]. 1.1 Manifolds and functions 1.2 Tangent vectors and vector fields 1.3 Covectors 1.4 Tensor algebra 1.5 Metrics 1.6 Differential forms 1.7 Maps and Lie derivative 1.8 Affine connection and covariant derivative 1.9 Matter couplings 1.10 Variations 1.11 Exercices 4
5 2 Variational principles for Einstein s equations This part follows exercises 1.4 and 3.17 of [6], chapter 21 of [7]. The application to 3d gravity follows [8] (see also [9]). The Einstein-Dirac application is taken from [10]. The discussion of Noether charges, identities and conserved n 2 forms is adapted from [11]. 2.1 Auxiliary fields and symmetries 2.2 Gauge symmetries 2.3 Metric formulation 2.4 Palatini formulation 2.5 Cartan formulation 2.6 Einstein-Dirac theory 2.7 3d gravity as a Chern-Simons theory 5
6 3 Newman-Penrose formalism This part follows closely [12] with some elements from [13]. A useful summary of the main results of this and the first chapter can be found in [14]. 3.1 Null basis and spin coefficients 3.2 Weyl, Ricci and Riemann tensor 3.3 Structure constants 3.4 Bianchi identities 3.5 Lorentz transformations and gauge fixation 3.6 Optical scalars 3.7 Petrov classification 3.8 Goldberg-Sachs theorem 6
7 4 Black holes This part follows mainly [15]. See also chapter 20 of [7], [16], [17], [18], [19], [20], [11], [21]. 4.1 Killing horizons 4.2 Schwarzschild black hole and Rindler spacetime 4.3 Kerr black hole 4.4 The first law of black hole mechanics 7
8 5 Asymptotics Some elementary results on symmetries of asymptotically flat and AdS spacetimes in d dimensions are presented. Original literature is [22], [23], [24], [25]. The presentation here is based on [26], [27]. 5.1 Asymptotic symmetries 8
9 6 Acknowledgements This work is supported in part by the Fund for Scientific Research-FNRS (Belgium) and by IISN-Belgium. References [1] G. Gibbons, Part III: Applications of Differential Geometry to Physics. Unpublished lecture notes, [2] T. Eguchi, P. B. Gilkey, and A. J. Hanson, Gravitation, gauge theories and differential geometry, Phys. Rept. 66 (1980) 213. [3] P. Spindel, Gravity before supergravity, in Supersymmetry, pp Springer, [4] B. Felsager, Geometry, particles, and fields. Springer Science & Business Media, [5] B. Schutz, Geometrical methods of mathematical physics. Cambridge University Press, [6] M. Henneaux and C. Teitelboim, Quantization of Gauge Systems. Princeton University Press, [7] C. Misner, K. Thorne, and J. Wheeler, Gravitation. W.H. Freeman, New York, [8] E. Witten, (2+1)-dimensional Gravity As An Exactly Soluble System, Nucl. Phys. B311 (1988) 46. [9] A. Achucarro and P. K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B180 (1986) 89. [10] M. Henneaux, Sur la géometrodynamique avec champs spinoriels. PhD thesis, Université Libre de Bruxelles, [11] G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B633 (2002) 3 82, hep-th/ [12] S. Chandrasekhar, The mathematical theory of black holes. Oxford University Press,
10 [13] J. Stewart, Advanced General Relativity. Cambridge University Press, [14] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein s field equations. Cambridge University Press, [15] P. K. Townsend, Black holes, gr-qc/ [16] J. M. Bardeen, B. Carter, and S. W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) [17] T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Ann. Phys. 88 (1974) 286. [18] R. M. Wald, Black hole entropy is Noether charge, Phys. Rev. D48 (1993) , gr-qc/ [19] V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D50 (1994) , gr-qc/ [20] V. Iyer and R. M. Wald, A comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D52 (1995) , gr-qc/ [21] E. Poisson, A Relativist s Toolkit. The Mathematics of Black-Hole Mechanics. Cambridge University Press, [22] R. K. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) [23] M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter spaces, Commun. Math. Phys. 98 (1985) 391. [24] J. D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: An example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207. [25] M. Henneaux, Asymptotically anti-de Sitter universes in d = 3, 4 and higher dimensions, in Proceedings of the Fourth Marcel Grossmann Meeting on General Relativity, Rome 1985, R. Ruffini, ed., pp Elsevier Science Publishers B.V., [26] G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062,
11 [27] G. Barnich and P.-H. Lambert, Einstein-Yang-Mills theory: Asymptotic symmetries, Phys.Rev. D88 (2013) ,
Theoretical Aspects of Black Hole Physics
Les Chercheurs Luxembourgeois à l Etranger, Luxembourg-Ville, October 24, 2011 Hawking & Ellis Theoretical Aspects of Black Hole Physics Glenn Barnich Physique théorique et mathématique Université Libre
More informationBMS current algebra and central extension
Recent Developments in General Relativity The Hebrew University of Jerusalem, -3 May 07 BMS current algebra and central extension Glenn Barnich Physique théorique et mathématique Université libre de Bruxelles
More informationLecture 2: 3d gravity as group theory Quantum Coulomb Solution
The Second Mandelstam Theoretical Physics School University of the Witwatersrand 17/01/2018 Lecture 2: 3d gravity as group theory Quantum Coulomb Solution Glenn Barnich Physique théorique et mathématique
More informationThree-dimensional gravity. Max Bañados Pontificia Universidad Católica de Chile
Max Bañados Pontificia Universidad Católica de Chile The geometry of spacetime is determined by Einstein equations, R µ 1 2 Rg µ =8 G T µ Well, not quite. The geometry is known once the full curvature
More informationBędlewo. October 19, Glenn Barnich. Physique théorique et mathématique. Université Libre de Bruxelles & International Solvay Institutes
Będlewo. October 19, 2007 Glenn Barnich Physique théorique et mathématique Université Libre de Bruxelles & International Solvay Institutes Algebraic structure of gauge systems: Theory and Applications
More informationAsymptotically flat spacetimes at null infinity revisited
QG2. Corfu, September 17, 2009 Asymptotically flat spacetimes at null infinity revisited Glenn Barnich Physique théorique et mathématique Université Libre de Bruxelles & International Solvay Institutes
More informationBibliography. Introduction to General Relativity and Cosmology Downloaded from
Bibliography Abbott, B. P. et al. (2016). Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102. Ade, P. A. R. et al. (2015). Planck 2015 results. XIII. Cosmological
More informationIntroductory Course on Black Hole Physics and AdS/CFT Duality Lecturer: M.M. Sheikh-Jabbari
Introductory Course on Black Hole Physics and AdS/CFT Duality Lecturer: M.M. Sheikh-Jabbari This is a PhD level course, designed for second year PhD students in Theoretical High Energy Physics (HEP-TH)
More informationSupplement to Lesson 9: The Petrov classification and the Weyl tensor
Supplement to Lesson 9: The Petrov classification and the Weyl tensor Mario Diaz November 1, 2015 As we have pointed out one of unsolved problems of General Relativity (and one that might be impossible
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v2 23 Feb 2004 100871 Beijing, China Abstract In this paper, complex
More informationConstrained BF theory as gravity
Constrained BF theory as gravity (Remigiusz Durka) XXIX Max Born Symposium (June 2010) 1 / 23 Content of the talk 1 MacDowell-Mansouri gravity 2 BF theory reformulation 3 Supergravity 4 Canonical analysis
More informationElectromagnetic Energy for a Charged Kerr Black Hole. in a Uniform Magnetic Field. Abstract
Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field Li-Xin Li Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (December 12, 1999) arxiv:astro-ph/0001494v1
More informationSpace-Times Admitting Isolated Horizons
Space-Times Admitting Isolated Horizons Jerzy Lewandowski Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Hoża 69, 00-681 Warszawa, Poland, lewand@fuw.edu.pl Abstract We characterize a general
More informationarxiv:hep-th/ v1 31 Jan 2006
hep-th/61228 arxiv:hep-th/61228v1 31 Jan 26 BTZ Black Hole with Chern-Simons and Higher Derivative Terms Bindusar Sahoo and Ashoke Sen Harish-Chandra Research Institute Chhatnag Road, Jhusi, Allahabad
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v3 10 Mar 2004 100871 Beijing, China Abstract In this paper, complex
More informationSnyder noncommutative space-time from two-time physics
arxiv:hep-th/0408193v1 25 Aug 2004 Snyder noncommutative space-time from two-time physics Juan M. Romero and Adolfo Zamora Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Apartado
More informationThermodynamics of black holes from the Hamiltonian point of view
Thermodynamics of black holes from the Hamiltonian point of view Ewa Czuchry Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-Oiwake-Cho, Sakyo-ku, Kyoto 606-8502, Japan Jacek
More informationAsymptotic Symmetries and Holography
Asymptotic Symmetries and Holography Rashmish K. Mishra Based on: Asymptotic Symmetries, Holography and Topological Hair (RKM and R. Sundrum, 1706.09080) Unification of diverse topics IR structure of QFTs,
More informationModern Geometric Structures and Fields
Modern Geometric Structures and Fields S. P. Novikov I.A.TaJmanov Translated by Dmitry Chibisov Graduate Studies in Mathematics Volume 71 American Mathematical Society Providence, Rhode Island Preface
More informationFourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007
Fourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007 Central extensions in flat spacetimes Duality & Thermodynamics of BH dyons New classical central extension in asymptotically
More informationContents. Preface to the second edition. Preface to the first edition. Part I Introduction to gravity and supergravity 1
Table of Preface to the second edition page xxi Preface to the first edition xxv Part I Introduction to gravity and supergravity 1 1 Differential geometry 3 1.1 World tensors 3 1.2 Affinely connected spacetimes
More informationAn introduction to General Relativity and the positive mass theorem
An introduction to General Relativity and the positive mass theorem National Center for Theoretical Sciences, Mathematics Division March 2 nd, 2007 Wen-ling Huang Department of Mathematics University of
More informationA Summary of the Black Hole Perturbation Theory. Steven Hochman
A Summary of the Black Hole Perturbation Theory Steven Hochman Introduction Many frameworks for doing perturbation theory The two most popular ones Direct examination of the Einstein equations -> Zerilli-Regge-Wheeler
More informationAn Introduction to General Relativity and Cosmology
An Introduction to General Relativity and Cosmology Jerzy Plebariski Centro de Investigacion y de Estudios Avanzados Instituto Politecnico Nacional Apartado Postal 14-740, 07000 Mexico D.F., Mexico Andrzej
More informationAspects of the BMS/CFT correspondence
DAMTP, Cambridge. February 17, 2010 Aspects of the BMS/CFT correspondence Glenn Barnich Physique théorique et mathématique Université Libre de Bruxelles & International Solvay Institutes So thank you for
More informationIntegrated Phd in Physical Sciences PH 516: General Relativity and Cosmology
Indian Association for the Cultivation of Science Department of Theoretical Physics Integrated Phd in Physical Sciences PH 516: General Relativity and Cosmology Instructor: Soumitra SenGupta and Sumanta
More informationNewman-Penrose s formalism
Available online at www.worldscientificnews.com WSN 96 (2018) 1-12 EISSN 2392-2192 Newman-Penrose s formalism P. Lam-Estrada 1, J. López-Bonilla 2, *, R. López-Vázquez 2, S. Vidal-Beltrán 2 1 ESFM, Instituto
More informationMy Personal Journey on the Geometric Aspect of General Relativity
My Personal Journey on the Geometric Aspect of General Relativity Shing-Tung Yau Harvard University The first annual meeting of ICCM 2017 Sun Yat-sen University, Guangzhou December 28, 2017 This talk is
More informationBlack Hole Entropy from Near Horizon Microstates
hep-th/9712251 HUTP-97/A106 Black Hole Entropy from Near Horizon Microstates Andrew Strominger Jefferson Laboratory of Physics Harvard University Cambridge, MA 02138 Abstract Black holes whose near horizon
More informationQuasi-local Mass in General Relativity
Quasi-local Mass in General Relativity Shing-Tung Yau Harvard University For the 60th birthday of Gary Horowtiz U. C. Santa Barbara, May. 1, 2015 This talk is based on joint work with Po-Ning Chen and
More informationTheoretical Aspects of Black Hole Physics
Les Chercheurs Luxembourgeois à l Etranger, Luxembourg-Ville, October 24, 2011 Hawking & Ellis Theoretical Aspects of Black Hole Physics Glenn Barnich Physique théorique et mathématique Université Libre
More informationMicroscopic entropy of the charged BTZ black hole
Microscopic entropy of the charged BTZ black hole Mariano Cadoni 1, Maurizio Melis 1 and Mohammad R. Setare 2 1 Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari arxiv:0710.3009v1
More informationHawking Emission and Black Hole Thermodynamics
Hawking Emission and Black Hole Thermodynamics arxiv:hep-th/0612193v1 18 Dec 2006 1 Introduction Don N. Page Theoretical Physics Institute Department of Physics, University of Alberta Room 238 CEB, 11322
More informationarxiv: v2 [hep-th] 6 Jun 2013
DAMTP-2013-9 Thermodynamics of exotic BTZ black holes Paul K. Townsend 1, and Baocheng Zhang 2, 1 Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University
More informationJose Luis Blázquez Salcedo
Jose Luis Blázquez Salcedo In collaboration with Jutta Kunz, Francisco Navarro Lérida, and Eugen Radu GR Spring School, March 2015, Brandenburg an der Havel 1. Introduction 2. General properties of EMCS-AdS
More informationTensor Calculus, Relativity, and Cosmology
Tensor Calculus, Relativity, and Cosmology A First Course by M. Dalarsson Ericsson Research and Development Stockholm, Sweden and N. Dalarsson Royal Institute of Technology Stockholm, Sweden ELSEVIER ACADEMIC
More informationarxiv: v2 [physics.gen-ph] 30 Dec 2014
arxiv:1411.2013v2 [physics.gen-ph] 30 Dec 2014 Plane Symmetric Cylindrically Symmetric and Spherically Symmetric Black hole Solutions of Einstein Field Equations Farhad Ali School of Natural Sciences National
More informationarxiv:hep-th/ v2 24 Sep 1998
Nut Charge, Anti-de Sitter Space and Entropy S.W. Hawking, C.J. Hunter and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom
More informationBlack Hole Physics. Basic Concepts and New Developments KLUWER ACADEMIC PUBLISHERS. Valeri P. Frolov. Igor D. Nbvikov. and
Black Hole Physics Basic Concepts and New Developments by Valeri P. Frolov Department of Physics, University of Alberta, Edmonton, Alberta, Canada and Igor D. Nbvikov Theoretical Astrophysics Center, University
More informationNon-existence of time-periodic dynamics in general relativity
Non-existence of time-periodic dynamics in general relativity Volker Schlue University of Toronto University of Miami, February 2, 2015 Outline 1 General relativity Newtonian mechanics Self-gravitating
More informationStatistical Entropy of the Four Dimensional Schwarzschild Black Hole
ULB TH 98/02 hep-th/98005 January 998 Statistical Entropy of the Four Dimensional Schwarzschild Black Hole R. Argurio, F. Englert 2 and L. Houart Service de Physique Théorique Université Libre de Bruxelles,
More informationHolography for 3D Einstein gravity. with a conformal scalar field
Holography for 3D Einstein gravity with a conformal scalar field Farhang Loran Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran. Abstract: We review AdS 3 /CFT 2 correspondence
More informationLecture Notes on General Relativity
Lecture Notes on General Relativity Matthias Blau Albert Einstein Center for Fundamental Physics Institut für Theoretische Physik Universität Bern CH-3012 Bern, Switzerland The latest version of these
More informationSolutions of Penrose s equation
JOURNAL OF MATHEMATICAL PHYSICS VOLUME 40, NUMBER 1 JANUARY 1999 Solutions of Penrose s equation E. N. Glass a) Physics Department, University of Michigan, Ann Arbor, Michigan 48109 Jonathan Kress School
More informationSupergravity. Abstract
Selfdual backgrounds in N = 2 five-dimensional Chern-Simons Supergravity Máximo Bañados Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile mbanados@maxwell.fis.puc.cl
More informationarxiv: v1 [gr-qc] 28 Mar 2012
Causality violation in plane wave spacetimes arxiv:103.6173v1 [gr-qc] 8 Mar 01 Keywords: vacuum spacetimes, closed null geodesics, plane wave spacetimes D. Sarma 1, M. Patgiri and F. Ahmed 3 Department
More informationRigidity of Black Holes
Rigidity of Black Holes Sergiu Klainerman Princeton University February 24, 2011 Rigidity of Black Holes PREAMBLES I, II PREAMBLE I General setting Assume S B two different connected, open, domains and
More informationCurved Spacetime III Einstein's field equations
Curved Spacetime III Einstein's field equations Dr. Naylor Note that in this lecture we will work in SI units: namely c 1 Last Week s class: Curved spacetime II Riemann curvature tensor: This is a tensor
More informationDoes the third law of black hole thermodynamics really have a serious failure?
Does the third law of black hole thermodynamics really have a serious failure? István Rácz KFKI Research Institute for Particle and Nuclear Physics H-1525 Budapest 114 P.O.B. 49, Hungary September 16,
More informationThermodynamics of a Black Hole with Moon
Thermodynamics of a Black Hole with Moon Laboratoire Univers et Théories Observatoire de Paris / CNRS In collaboration with Sam Gralla Phys. Rev. D 88 (2013) 044021 Outline ➀ Mechanics and thermodynamics
More informationTwistors, amplitudes and gravity
Twistors, amplitudes and gravity From twistor strings to quantum gravity? L.J.Mason The Mathematical Institute, Oxford lmason@maths.ox.ac.uk LQG, Zakopane 4/3/2010 Based on JHEP10(2005)009 (hep-th/0507269),
More information8 Symmetries and the Hamiltonian
8 Symmetries and the Hamiltonian Throughout the discussion of black hole thermodynamics, we have always assumed energy = M. Now we will introduce the Hamiltonian formulation of GR and show how to define
More informationarxiv:gr-qc/ v1 11 Oct 1999
NIKHEF/99-026 Killing-Yano tensors, non-standard supersymmetries and an index theorem J.W. van Holten arxiv:gr-qc/9910035 v1 11 Oct 1999 Theoretical Physics Group, NIKHEF P.O. Box 41882, 1009 DB Amsterdam
More informationBlack Holes, Integrable Systems and Soft Hair
Ricardo Troncoso Black Holes, Integrable Systems and Soft Hair based on arxiv: 1605.04490 [hep-th] In collaboration with : A. Pérez and D. Tempo Centro de Estudios Científicos (CECs) Valdivia, Chile Introduction
More informationJose Luis Blázquez Salcedo
Physical Review Letters 112 (2014) 011101 Jose Luis Blázquez Salcedo In collaboration with Jutta Kunz, Eugen Radu and Francisco Navarro Lérida 1. Introduction: Ansatz and general properties 2. Near-horizon
More informationAngular momentum and Killing potentials
Angular momentum and Killing potentials E. N. Glass a) Physics Department, University of Michigan, Ann Arbor, Michigan 4809 Received 6 April 995; accepted for publication September 995 When the Penrose
More informationEffect of Monopole Field on the Non-Spherical Gravitational Collapse of Radiating Dyon Solution.
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn:2319-765x. Volume 10, Issue 1 Ver. III. (Feb. 2014), PP 46-52 Effect of Monopole Field on the Non-Spherical Gravitational Collapse of Radiating
More information9 Symmetries of AdS 3
9 Symmetries of AdS 3 This section consists entirely of exercises. If you are not doing the exercises, then read through them anyway, since this material will be used later in the course. The main goal
More informationRelativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION. Wolfgang Rindler. Professor of Physics The University of Texas at Dallas
Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION Wolfgang Rindler Professor of Physics The University of Texas at Dallas OXPORD UNIVERSITY PRESS Contents Introduction l 1 From absolute space
More informationRELG - General Relativity
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2017 230 - ETSETB - Barcelona School of Telecommunications Engineering 749 - MAT - Department of Mathematics 748 - FIS - Department
More informationSELF-SIMILAR PERFECT FLUIDS
SELF-SIMILAR PERFECT FLUIDS J. CAROT and A.M. SINTES Departament de Física, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain Space-times admitting an r-parameter Lie group of homotheties
More informationPRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in
LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific
More informationClassical aspects of Poincaré gauge theory of gravity
Classical aspects of Poincaré gauge theory of gravity Jens Boos jboos@perimeterinstitute.ca Perimeter Institute for Theoretical Physics Wednesday, Nov 11, 2015 Quantum Gravity group meeting Perimeter Institute
More informationFirst structure equation
First structure equation Spin connection Let us consider the differential of the vielbvein it is not a Lorentz vector. Introduce the spin connection connection one form The quantity transforms as a vector
More informationHIGHER SPIN ADS 3 GRAVITIES AND THEIR DUAL CFTS
HIGHER SPIN ADS 3 GRAVITIES AND THEIR DUAL CFTS Yasuaki Hikida (Keio University) Based on [1] JHEP02(2012)109 [arxiv:1111.2139 [hep-th]] [2] arxiv:1209.xxxx with Thomas Creutzig (Tech. U. Darmstadt) Peter
More information1. Introduction A few years ago, Ba~nados, Teitelboim and Zanelli (BTZ) showed that three-dimensional General Relativity with a negative cosmological
STATIONARY BLACK HOLES IN A GENERALIZED THREE-DIMENSIONAL THEORY OF GRAVITY Paulo M. Sa Sector de Fsica, Unidade de Ci^encias Exactas e Humanas, Universidade do Algarve, Campus de Gambelas, 8000 Faro,
More informationA note on covariant action integrals in three dimensions
A note on covariant action integrals in three dimensions Máximo Bañados 1,2, and Fernando Méndez 2,3 1 Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza 50009, Spain
More informationGeometric inequalities for black holes
Geometric inequalities for black holes Sergio Dain FaMAF-Universidad Nacional de Córdoba, CONICET, Argentina. 3 August, 2012 Einstein equations (vacuum) The spacetime is a four dimensional manifold M with
More informationAcc. Sc. Torino Atti Sc. Fis. 149 (2015), 17-34
Acc. Sc. Torino Atti Sc. Fis. 149 (2015), 17-34 Commemorazioni di Accademici in unità h/2 pi greco stesse unità Commemorazioni di Accademici f(e, cos theta) l+1/2 i poli di Regge Potential Scattering Commemorazioni
More informationGravitational Gauge Theory and the Existence of Time
Journal of Physics: Conference Series OPEN ACCESS Gravitational Gauge Theory and the Existence of Time To cite this article: James T Wheeler 2013 J. Phys.: Conf. Ser. 462 012059 View the article online
More informationOutline. 1 Relativistic field theory with variable space-time. 3 Extended Hamiltonians in field theory. 4 Extended canonical transformations
Outline General Relativity from Basic Principles General Relativity as an Extended Canonical Gauge Theory Jürgen Struckmeier GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany j.struckmeier@gsi.de,
More informationCurved Spacetime I. Dr. Naylor
Curved Spacetime I Dr. Naylor Last Week Einstein's principle of equivalence We discussed how in the frame of reference of a freely falling object we can construct a locally inertial frame (LIF) Space tells
More informationThe Horizon Energy of a Black Hole
arxiv:1712.08462v1 [gr-qc] 19 Dec 2017 The Horizon Energy of a Black Hole Yuan K. Ha Department of Physics, Temple University Philadelphia, Pennsylvania 19122 U.S.A. yuanha@temple.edu December 1, 2017
More informationQuasi-local Mass and Momentum in General Relativity
Quasi-local Mass and Momentum in General Relativity Shing-Tung Yau Harvard University Stephen Hawking s 70th Birthday University of Cambridge, Jan. 7, 2012 I met Stephen Hawking first time in 1978 when
More informationarxiv: v2 [gr-qc] 5 Sep 2018
SCALAR POLYNOMIAL CURVATURE INVARIANTS IN THE CONTEXT OF THE CARTAN-KARLHEE ALGORITHM arxiv:1506.03415v2 [gr-qc] 5 Sep 2018. A. BROOKS 1,.. MCNUTT 1,3, J. P. SIMAR 2, AN N. K. MUSOKE 1,4 1 EPARTMENT OF
More informationConnection Variables in General Relativity
Connection Variables in General Relativity Mauricio Bustamante Londoño Instituto de Matemáticas UNAM Morelia 28/06/2008 Mauricio Bustamante Londoño (UNAM) Connection Variables in General Relativity 28/06/2008
More informationAn introduction to gravitational waves. Enrico Barausse (Institut d'astrophysique de Paris/CNRS, France)
An introduction to gravitational waves Enrico Barausse (Institut d'astrophysique de Paris/CNRS, France) Outline of lectures (1/2) The world's shortest introduction to General Relativity The linearized
More informationarxiv:gr-qc/ v1 26 Aug 1997
Action and entropy of lukewarm black holes SNUTP 97-119 Rong-Gen Cai Center for Theoretical Physics, Seoul National University, Seoul, 151-742, Korea arxiv:gr-qc/9708062v1 26 Aug 1997 Jeong-Young Ji and
More informationEntanglement and the Bekenstein-Hawking entropy
Entanglement and the Bekenstein-Hawking entropy Eugenio Bianchi relativity.phys.lsu.edu/ilqgs International Loop Quantum Gravity Seminar Black hole entropy Bekenstein-Hawking 1974 Process: matter falling
More informationNewman-Penrose formalism in higher dimensions
Newman-Penrose formalism in higher dimensions V. Pravda various parts in collaboration with: A. Coley, R. Milson, M. Ortaggio and A. Pravdová Introduction - algebraic classification in four dimensions
More informationThermodynamics in modified gravity Reference: Physics Letters B 688, 101 (2010) [e-print arxiv: [gr-qc]]
Thermodynamics in modified gravity Reference: Physics Letters B 688, 101 (2010) [e-print arxiv:0909.2159 [gr-qc]] HORIBA INTERNATIONAL CONFERENCE COSMO/CosPA 2010 Hongo campus (Koshiba Hall), The University
More informationMatrix Approach to Petrov Classification
Matrix Approach to Petrov Classification B. E. Carvajal-Gámez 1, J. López-Bonilla *2 & R. López-Vázquez 2 151 Article 1 SEPI-ESCOM, Instituto Politécnico Nacional (IPN), Av. Bátiz S/N, 07738, México DF
More informationNon-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes
Non-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes arxiv:hep-th/0311221v2 17 Jan 2004 M.R. Setare Physics Dept. Inst. for Studies in Theo. Physics and Mathematics(IPM) P. O. Box 19395-5531,
More informationOn the Geometry of Planar Domain Walls. F. M. Paiva and Anzhong Wang y. Abstract. The Geometry of planar domain walls is studied.
On the Geometry of Planar Domain Walls F. M. Paiva and Anzhong Wang y Departmento de Astrofsica, Observatorio Nacional { CNPq, Rua General Jose Cristino 77, 091-400 Rio de Janeiro { RJ, Brazil Abstract
More informationDynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory
hep-th/9707042 MRI-PHY/P970716 Dynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory Ashoke Sen 1 2 Mehta Research Institute of Mathematics and Mathematical Physics Chhatnag Road, Jhusi,
More informationarxiv: v1 [gr-qc] 9 Jul 2009
Properties of kinematic singularities arxiv:0907.1620v1 [gr-qc] 9 Jul 2009 A A Coley, Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 Email: aac@mathstat.dal.ca
More informationarxiv: v1 [gr-qc] 16 Jul 2014
An extension of the Newman-Janis algorithm arxiv:1407.4478v1 [gr-qc] 16 Jul 014 1. Introduction Aidan J Keane 4 Woodside Place, Glasgow G3 7QF, Scotland, UK. E-mail: aidan@worldmachine.org Abstract. The
More information31st Jerusalem Winter School in Theoretical Physics: Problem Set 2
31st Jerusalem Winter School in Theoretical Physics: Problem Set Contents Frank Verstraete: Quantum Information and Quantum Matter : 3 : Solution to Problem 9 7 Daniel Harlow: Black Holes and Quantum Information
More informationThe Black Hole in Three Dimensional. Spacetime
arxiv:hep-th/9204099v3 20 Mar 2001 The Black Hole in Three Dimensional Spacetime Máximo Bañados (1,a) Claudio Teitelboim (1,2,a) and Jorge Zanelli (1,a) (1) Centro de Estudios Científicos de Santiago,
More informationPurely magnetic vacuum solutions
Purely magnetic vacuum solutions Norbert Van den Bergh Faculty of Applied Sciences TW16, Gent University, Galglaan, 9000 Gent, Belgium 1. Introduction Using a +1 formalism based on a timelike congruence
More informationThe Hamiltonian formulation of gauge theories
The Hamiltonian formulation of gauge theories I [p, q] = dt p i q i H(p, q) " # q i = @H @p i =[q i, H] ṗ i = @H =[p @q i i, H] 1. Symplectic geometry, Hamilton-Jacobi theory,... 2. The first (general)
More informationarxiv:hep-ph/ v1 8 Feb 2000
Gravity, Particle Physics and their Unification 1 J. M. Maldacena Department of Physics Harvard University, Cambridge, Massachusetts 02138 arxiv:hep-ph/0002092v1 8 Feb 2000 1 Introduction Our present world
More informationBlack Strings and Classical Hair
UCSBTH-97-1 hep-th/97177 Black Strings and Classical Hair arxiv:hep-th/97177v1 17 Jan 1997 Gary T. Horowitz and Haisong Yang Department of Physics, University of California, Santa Barbara, CA 9316, USA
More informationThermodynamics of spacetime in generally covariant theories of gravitation
Thermodynamics of spacetime in generally covariant theories of gravitation Christopher Eling Department of Physics, University of Maryland, College Park, MD 20742-4111, USA draft of a paper for publication
More informationarxiv: v2 [gr-qc] 7 Jan 2019
Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory arxiv:1810.03411v2 [gr-qc] 7 Jan 2019 Metin Gürses 1, and Bayram Tekin 2, 1 Department of Mathematics, Faculty of Sciences Bilkent
More informationWave function of the quantum black hole
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/221666470 Wave function of the quantum black hole ARTICLE in PHYSICS LETTERS B FEBRUARY 2012
More informationarxiv:gr-qc/ v1 6 Dec 2000
Initial data for two Kerr-lie blac holes Sergio Dain Albert-Einstein-Institut, Max-Planc-Institut für Gravitationsphysi, Am Mühlenberg 1, D-14476 Golm, Germany (April 5, 2004) We prove the existence of
More informationHigher-Spin Fermionic Gauge Fields & Their Electromagnetic Coupling
Higher-Spin Fermionic Gauge Fields & Their Electromagnetic Coupling Rakibur Rahman Université Libre de Bruxelles, Belgium March 28, 2012 CQUeST Workshop on Higher Spins & String Geometry Sogang University,
More informationGRAVITATIONAL COLLAPSE AND RELATIVITY
Proceedings of Yamada Conference XIV GRAVITATIONAL COLLAPSE AND RELATIVITY KYOTO INTERNATIONAL CONFERENCE HALL, JAPAN 7-11 APRIL 1986 EDITED BY HUMITAKA SATO TAKASHI NAKAMURA UNIVERSITATSBIBLIOTHEK HANNOVER
More informationHolography and phase-transition of flat space
Holography and phase-transition of flat space Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Workshop on Higher-Spin and Higher-Curvature Gravity, São Paulo, 4. November
More information