Gravity and the thermodynamics of horizons

Physics Reports

Volumn 406, Issue 2, 2005, Pages 49-125

  Padmanabhan, T ^a  

^a INTER UNIVERSITY CENTRE FOR ASTRONOMY AND ASTROPHYSICS   (India)

Author keywords

Black hole; Einstein Hilbert action; Entropy; Horizon; Quantum theory

Indexed keywords

EID: 14944365360     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2004.10.003     Document Type: Review

References (179)

1. Eddington, Space, Time and Gravitation, Cambridge University Press, UK, 1920.
2. P.A.M. Dirac Proc. Roy. Soc (London) A 270 1962 354
3. J.M. Bardeen B. Carter S.W. Hawking The four laws of black hole mechanics Commun. Math. Phys. 31 1973 161-170
4. C. DeWitt, B. DeWitt (Eds.), Black Holes, University of Grenobe, 1972.
5. K.S. Thorne, R.H. Price, D.A. Macdonald (Eds.), Black Holes: The Membrane Paradigm, Yale University Press, London, 1986.
6. J.D. Bekenstein Black holes and the second law Nuovo Cim. Lett. 4 1972 737-740
7. J.D. Bekenstein Black holes and entropy Phys. Rev. D 7 1973 2333-2346
8. J.D. Bekenstein Generalized second law of thermodynamics in black hole physics Phys. Rev. D 9 1974 3292-3300
9. S.W. Hawking Particle creation by black holes Commun. Math. Phys. 43 1975 199-220
10. S.A. Fulling Nonuniqueness of canonical field quantization in riemannian space-time Phys. Rev. D 7 1973 2850-2862
11. P.C.W. Davies Scalar particle production in schwarzschild and rindler metrics J. Phys. A 8 1975 609-616
12. U.H. Gerlach The mechanism of blackbody radiation from an incipient black hole Phys. Rev. D 14 1976 1479-1508
13. C. Misner K. Thorne J. Wheeler Gravitation 1973 Freeman and Co. New York
14. N.D. Birrel P.C.W. Davies Quantum Field Theory in Curved Space-Time 1982 Cambridge University Press Cambridge
15. S.A. Fulling Aspects of Quantum Field Theory in Curved Space-Time 1989 Cambridge University Press Cambridge
16. R.M. Wald Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics 1994 The University of Chicago Press Chicago
17. B.S. Dewitt Quantum field theory in curved space-time Phys. Rep. 19 1975 295-357
18. S. Takagi Vacuum noise and stress induced by uniform accelerator: Hawking-unruh effect in rindler manifold of arbitrary dimensions Prog. Theor. Phys. Suppl. 88 1986 1-142
19. L. Sriramkumar T. Padmanabhan Probes of the vacuum structure of quantum fields in classical backgrounds Int. J. Mod. Phys. D 11 2002 1-34
20. R. Bousso The holographic principle Rev. Mod. Phys. 74 2002 825-874
21. R. Brout S. Massar R. Parentani P. Spindel A primer for black hole quantum physics Phys. Rep. 260 1995 329-454
22. R.M. Wald The thermodynamics of black holes Living Rev. Rel. 4 2001 6
23. D.W. Sciama P. Candelas D. Deutsch Quantum field theory, horizons and thermodynamics Adv. Phys. 30 1981 327-366
24. S.W. Hawking G.F.R. Ellis The Large Scale Structure of Space-time 1973 Cambridge University Press Cambridge
25. J.R. Letaw J.D. Pfautsch The quantized scalar field in the stationary coordinate systems of flat space-time Phys. Rev. D 24 1981 1491
26. J.R. Letaw Vacuum excitation of noninertial detectors on stationary world lines Phys. Rev. D 23 1981 1709
27. T. Padmanabhan General covariance, accelerated frames and the particle concept Astrophys. Sp. Sci. 83 1982 247
28. L. Landau E.M. Lifshitz Classical Theory of Field vol. II 1975 Pergamon Press New York
29. A. Ashtekar B. Krishnan Dynamical horizons and their properties Phys. Rev. D 68 2003 104 030
30. G. Date Isolated horizon, killing horizon and event horizon Class. Quant. Grav. 18 2001 5219-5226
31. P.G. Grove On an inertial observer's interpretation of the detection of radiation by linearly accelerated particle detectors Class. Quant. Grav. 3 1986 801-809
32. B.L. Hu A. Raval Thermal radiance from black hole and cosmological space-times: A unified view Mod. Phys. Lett. A 11 1996 2625-2638
33. D. Koks B.L. Hu A. Matacz A. Raval Thermal particle creation in cosmological spacetimes: A stochastic approach Phys. Rev. D 56 1997 4905-4915
34. B.L. Hu, Hawking-unruh thermal radiance as relativistic exponential scaling of quantum noise, (gr-qc / 9606073) 1996.
35. A. Raval B.L. Hu D. Koks Near-thermal radiation in detectors mirrors and black holes: A stochastic approach Phys. Rev. D 55 1997 4795-4812
36. M. Visser Essential and inessential features of hawking radiation Int. J. Mod. Phys. D 12 2003 649-661
37. K. Srinivasan L. Sriramkumar T. Padmanabhan Plane waves viewed from an accelerated frame: Quantum physics in classical setting Phys. Rev. D 56 1997 6692
38. K. Srinivasan L. Sriramkumar T. Padmanabhan Possible quantum interpretation of certain power spectra in classical field theory Int. J. Mod. Phys. D 6 1997 607-623
39. T. Padmanabhan Thermodynamics and/of horizons: A comparison of schwarzschild, rindler and de sitter spacetimes Mod. Phys. Lett. A 17 2002 923-942
40. J.D. Bekenstein Black holes: Classical properties, thermodynamics, and heuristic quantization In: M. Novello (Eds.) Cosmology and Gravitation 2000 Atlantisciences France 1-85
41. K. Srinivasan T. Padmanabhan Particle production and complex path analysis Phys. Rev. D 60 1999 024007
42. S. Carlip Entropy from conformal field theory at killing horizons Class. Quant. Grav. 16 1999 3327-3348
43. M.-I. Park J. Ho Comments on 'black hole entropy from conformal field theory in any dimension' Phys. Rev. Lett. 83 1999 5595
44. M.-I. Park Hamiltonian dynamics of bounded spacetime and black hole entropy: Canonical method Nucl. Phys. B 634 2002 339-369
45. Y.-b. Kim, C.Y. Oh, N. Park, Classical geometry of de sitter spacetime: an introductory review, 2002 (hep-th / 0212326)
46. G. Gibbons S. Hawking Cosmological event horizons, thermodynamics, and particle creation Phys. Rev. D 15 1977 2738-2751
47. R. Feynman The reason for anti-particle In: R. Feynman S. Weinberg (Eds.) Elementary Particles and the Laws of Physics, The 1986 Dirac Memorial Lectures 1988 Cambridge University Press Cambridge 1-59
48. L. Parker Particle creation in expanding universes Phys. Rev. Lett. 21 1968 562-564
49. L. Parker Quantized fields and particle creation in expanding universes. 1 Phys. Rev. 183 1969 1057-1068
50. T. Damour R. Ruffini Black-hole evaporation in the klein-sauter-heisenberg-euler formalism Phys. Rev. D 14 1976 332
51. J.B. Hartle S.W. Hawking Path integral derivation of black hole radiance Phys. Rev. D 13 1976 2188-2203
52. G.W. Gibbons S.W. Hawking Action integrals and partition functions in quantum gravity Phys. Rev. D 15 1977 2752-2756
53. M.K. Parikh F. Wilczek Hawking radiation as tunneling Phys. Rev. Lett. 85 2000 5042-5045
54. S. Shankaranarayanan K. Srinivasan T. Padmanabhan Method of complex paths and general covariance of hawking radiation Mod. Phys. Lett. A 16 2001 571-578
55. S. Shankaranarayanan T. Padmanabhan K. Srinivasan Hawking radiation in different coordinate settings: Complex paths approach Class. Quant. Grav. 19 2002 2671-2688
56. R. Schutzhold On the hawking effect Phys. Rev. D 64 2001 024029
57. S.M. Christensen M.J. Duff Flat space as a gravitational instanton Nucl. Phys. B 146 1978 11
58. W. Troost H. van Dam Thermal propagators and accelerated frames of reference Nucl. Phys. B 152 1979 442
59. T. Padmanabhan Topological interpretation of the horizon temperature Mod. Phys. Lett. A 18 2003 2903
60. W.G. Unruh Notes on black hole evaporation Phys. Rev. D 14 1976 870
61. T. Padmanabhan Entropy of horizons complex paths and quantum tunneling, Mod. Phys. Lett. A 19 2004 2637-2643
62. E. Keski-Vakkuri P. Kraus Microcanonical d-branes and back reaction Nucl. Phys. B 491 1997 249-262
63. A.J.M. Medved Radiation via tunneling from a de sitter cosmological horizon Phys. Rev. D 66 2002 124009
64. L. Landau, E.M. Lifshitz, Course of Theoretical Physics, vol. III, Quantum Mechanics, Pergamon Press, New York, 1977.
65. T.D. Lee Are black holes blackbodies? Nucl. Phys. B 264 1986 437
66. W.G. Unruh N. Weiss Acceleration radiation in interacting field theories Phys. Rev. D 29 1984 1656
67. U.H. Gerlach Quantum states of a field partitioned by an accelerated frame Phys. Rev. D 40 1989 1037-1047
68. B.S. DeWitt Quantum gravity: The new synthesis In: S. Hawking W. Israel (Eds.) General Relativity: An Einstein Centenary Survey 1979 Cambridge University Press Cambridge 680-745
69. P.G. Grove A.C. Ottewill Notes on 'particle detectors' J. Phys. A 16 1983 3905-3920
70. T. Padmanabhan Why does an accelerated detector click? Class. Quan. Grav. 2 1985 117
71. T. Padmanabhan Cosmological constant: The weight of the vacuum Phys. Rep. 380 2003 235-320
72. T. Padmanabhan T.R. Choudhury Can the clustered dark matter and the smooth dark energy arise from the same scalar field? Phys. Rev. D 66 2002 081301
73. T.R. Choudhury, T. Padmanabhan, Cosmological parameters from supernova observations: A critical comparison of three data sets, Astron. Astrophys., in press (astro-ph / 0311622).
74. D.G. Boulware Quantum field theory in schwarzschild and rindler spaces Phys. Rev. D 11 1975 1404
75. T. Padmanabhan Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes Class. Quant. Grav. 19 2002 5387-5408
76. T.M. Davis P.C.W. Davies C.H. Lineweaver Black hole versus cosmological horizon entropy Class. Quant. Grav. 20 2003 2753-2764
77. P.C.W. Davies, T.M. Davis, How far can the generalized second law be generalized? 2003 (astro-ph / 0310522).
78. S. Deser O. Levin Accelerated detectors and temperature in (anti) de sitter spaces Class. Quant. Grav. 14 1997 L163-L168
79. S. Deser O. Levin Mapping hawking into unruh thermal properties Phys. Rev. D 59 1999 064004
80. T.R. Choudhury, T. Padmanabhan, Concept of temperature in multi-horizon spacetimes: Analysis of schwarzschild-de sitter metric, 2004 (gr-qc / 0404091).
81. D. Markovic W.G. Unruh Vacuum for a massless scalar field outside a collapsing body in de sitter space-time Phys. Rev. D 43 1991 332-339
82. S. Tadaki S. Takagi Quantum field theory in two-dimensional schwarzschild-de sitter space-time. 2: Space with a collapsing star Prog. Theor. Phys. 83 1990 1126-1139
83. S.-I. Tadaki S. Takagi Quantum field theory in two-dimensional schwarzschild-de sitter space-time 1. empty space Prog. Theor. Phys. 83 1990 941-952
84. W.G. Unruh R.M. Wald Acceleration radiation and generalized second law of thermodynamics Phys. Rev. D 25 1982 942-958
85. V.P. Frolov D.N. Page Proof of the generalized second law for quasistationary semiclassical black holes Phys. Rev. Lett. 71 1993 3902-3905
86. T. Padmanabhan Statistical mechanics of gravitating systems Phys. Rep. 188 1990 285
87. U.H. Gerlach Why is a black hole hot? Phys. Rev. D 14 1976 3290-3293
88. S.W. Hawking Black holes and thermodynamics Phys. Rev. D 13 1976 191-197
89. J.D. Bekenstein Statistical black hole thermodynamics Phys. Rev. D 12 1975 3077-3085
90. J.A. Wheeler A Journey into Gravity and Spacetime 1990 Freeman and Co. NY
91. G. 't Hooft The black hole interpretation of string theory Nucl. Phys. B 335 1990 138-154
92. L. Susskind L. Thorlacius J. Uglum The stretched horizon and black hole complementarity Phys. Rev. D 48 1993 3743-3761
93. R.M. Wald Black hole entropy in noether charge Phys. Rev. D 48 1993 3427-3431
94. T. Jacobson G. Kang R.C. Myers On black hole entropy Phys. Rev. D 49 1994 6587-6598
95. M. Visser Dirty black holes: Entropy as a surface term Phys. Rev. D 48 1993 5697-5705
96. M. Banados C. Teitelboim J. Zanelli Black hole entropy and the dimensional continuation of the gauss-bonnet theorem Phys. Rev. Lett. 72 1994 957-960
97. L. Susskind Some speculations about black hole entropy in string theory In: C. Teitelboim (Eds.) The black hole, 25 years after 1998 World Scientific Singapore 118-131
98. J.S. Dowker Remarks on geometric entropy Class. Quant. Grav. 11 1994 L55-L60
99. W. Israel Thermo field dynamics of black holes Phys. Lett. A 57 1976 107-110
100. J. Callan G. Curtis F. Wilczek On geometric entropy Phys. Lett. B 333 1994 55-61
101. V.P. Frolov D.V. Fursaev Thermal fields, entropy, and black holes Class. Quant. Grav. 15 1998 2041-2074
102. V.P. Frolov D.V. Fursaev Mechanism of generation of black hole entropy in sakharov's induced gravity Phys. Rev. D 56 1997 2212-2225
103. V.P. Frolov D.V. Fursaev A.I. Zelnikov Statistical origin of black hole entropy in induced gravity Nucl. Phys. B 486 1997 339-352
104. W.G. Unruh Sonic analog of black holes and the effects of high frequencies on black hole evaporation Phys. Rev. D 51 1995 2827-2838
105. T. Jacobson Black hole radiation in the presence of a short distance cutoff Phys. Rev. D 48 1993 728-741
106. R. Brout S. Massar R. Parentani P. Spindel Hawking radiation without transplanckian frequencies Phys. Rev. D 52 1995 4559-4568
107. G. 't Hooft On the quantum structure of a black hole Nucl. Phys. B 256 1985 727
108. T. Padmanabhan On the quantum structure of horizons Phys. Lett. B 173 1986 43-45
109. V. Frolov I. Novikov Dynamical origin of the entropy of a black hole Phys. Rev. D 48 1993 4545-4551
110. W.H. Zurek K.S. Thorne Statistical mechanical origin of the entropy of a rotating, charged black hole Phys. Rev. Lett. 54 1985 2171
111. L. Bombelli R.K. Koul J.-H. Lee R.D. Sorkin A quantum source of entropy for black holes Phys. Rev. D 34 1986 373
112. M. Srednicki Entropy and area Phys. Rev. Lett. 71 1993 666-669
113. T. Padmanabhan Quantum structure of spacetime and black hole entropy Phys. Rev. Lett. 81 1998 4297-4300
114. T. Padmanabhan Event horizon: Magnifying glass for planck length physics Phys. Rev. D 59 1999 124012
115. W.G. Unruh, Dumb holes and the effects of high frequencies on black hole evaporation, 1994 (gr-qc / 9409008).
116. S. Corley T. Jacobson Hawking spectrum and high frequency dispersion Phys. Rev. D 54 1996 1568-1586
117. R.C. Myers Pure states don't wear black Gen. Rel. Grav. 29 1997 1217-1222
118. C. Rovelli Loop quantum gravity Living Rev. Rel. 1 1998 1
119. S.R. Das S.D. Mathur The quantum physics of black holes: Results from string theory Ann. Rev. Nucl. Part. Sci. 50 2000 153-206
120. A.W. Peet Tasi lectures on black holes in string theory in: Boulder 1999, Strings Branes, and Gravity 1999 353-433hep-th/0008241
121. A. Strominger C. Vafa Microscopic origin of the bekenstein-hawking entropy Phys. Lett. B 379 1996 99-104
122. J.C. Breckenridge et al. Macroscopic and microscopic entropy of near-extremal spinning black holes Phys. Lett. B 381 1996 423-426
123. A. Sen Dyon-monopole bound states, selfdual harmonic forms on the multi-monopole moduli space, and sl(2,z) invariance in string theory Phys. Lett. B 329 1994 217-221
124. C. Vafa E. Witten A strong coupling test of s duality Nucl. Phys. B 431 1994 3-77
125. A. Sen, Non-bps states and branes in string theor, in: Cargese 1999, Progress in String Theory and M -theory, 3rd APCTP Winter School on Duality in Fields and Strings, 1999, pp. 187-234 (hep-th/9904207).
126. C. Rovelli, P. Upadhya, Loop quantum gravity and quanta of space: A primer, 1998 (gr-qc/9806079).
127. T. Thiemann, Introduction to modern canonical quantum general relativity, submitted to Living Rev. Rel. 2001 (gr-qc/0110034).
128. K.V. Krasnov On statistical mechanics of gravitational systems Gen. Rel. Grav. 30 1998 53-68
129. C. Rovelli Black hole entropy from loop quantum gravity Phys. Rev. Lett. 77 1996 3288-3291
130. A. Ashtekar J.C. Baez K. Krasnov Quantum geometry of isolated horizons and black hole entropy Adv. Theor. Math. Phys. 4 2000 1-94
131. A. Ashtekar J. Baez A. Corichi K. Krasnov Quantum geometry and black hole entropy Phys. Rev. Lett. 80 1998 904-907
132. A. Corichi On quasinormal modes, black hole entropy, and quantum geometry Phys. Rev. D 67 2003 087502
133. K.D. Kokkotas B.G. Schmidt Quasi-normal modes of stars and black holes Living Rev. Rel. 2 1999 2
134. E. Berti V. Cardoso K.D. Kokkotas H. Onozawa Highly damped quasinormal modes of kerr black holes Phys. Rev. D 68 2003 124018
135. V. Cardoso J.P.S. Lemos S. Yoshida Quasinormal modes of schwarzschild black holes in four and higher dimensions Phys. Rev. D 69 2004 044004
136. T. Padmanabhan Quasi normal modes: A simple derivation of the level spacing of the frequencies Class. Quant. Grav. 21 2004 L1
137. T.R. Choudhury T. Padmanabhan Quasi normal modes in schwarzschild-desitter spacetime: A simple derivation of the level spacing of the frequencies Phys. Rev. D 69 2004 064033
138. L. Motl A. Neitzke Asymptotic black hole quasinormal frequencies Adv. Theor. Math. Phys. 7 2003 307-330
139. L. Motl An analytical computation of asymptotic schwarzschild quasinormal frequencies Adv. Theor. Math. Phys. 6 2003 1135-1162
140. O. Dreyer Quasinormal modes, the area spectrum, and black hole entropy Phys. Rev. Lett. 90 2003 081301
141. S. Hod Bohr's correspondence principle and the area spectrum of quantum black holes Phys. Rev. Lett. 81 1998 4293
142. T. Padmanabhan, A. Patel, Role of horizons in semiclassical gravity: entropy and the area spectrum, 2003 (gr-qc / 0309053).
143. T. Padmanabhan Why gravity has no choice: Bulk spacetime dynamics is dictated by information entanglement across horizons Gen. Rel. Grav. 35 2003 2097-2103
144. J. York W. James Black hole thermodynamics and the euclidean einstein action Phys. Rev. D 33 1986 2092-2099
145. H.W. Braden J.D. Brown B.F. Whiting J. York W. James Charged black hole in a grand canonical ensemble Phys. Rev. D 42 1990 3376-3385
146. J.D. Brown E.A. Martinez J. York W. James Complex kerr-newman geometry and black hole thermodynamics Phys. Rev. Lett. 66 1991 2281-2284
147. E.A. Martinez J. York W. James Additivity of the entropies of black holes and matter in equilibrium Phys. Rev. D 40 1989 2124-2127
148. G. Hayward Euclidean action and the thermodynamics of manifolds without boundary Phys. Rev. D 41 1990 3248-3251
149. G. Hayward General first law and thermodynamics of horizon / matter systems Phys. Rev. D 43 1991 3861-3872
150. T. Jacobson Thermodynamics of space-time: The Einstein equation of state Phys. Rev. Lett. 75 1995 1260-1263
151. G.E. Volovik Superfluid analogies of cosmological phenomena Phys. Rep. 351 2001 195-348
152. G.E. Volovik The Universe in a Helium Droplet 2003 Oxford University Press UK
153. J.D. Brown Black hole entropy and the hamiltonian formulation of diffeomorphism invariant theories Phys. Rev. D 52 1995 7011-7026
154. T. Padmanabhan Is gravity an intrinsically quantum phenomenon? dynamics of gravity from the entropy of spacetime and the principle of equivalence Mod. Phys. Lett. A 17 2002 1147-1158
155. T. Padmanabhan Gravity from spacetime thermodynamics Astrophys. Sp. Sci. 285 2003 407
156. T. Padmanabhan, From gravitons to gravity: Myths and reality, 2004 (gr-qc / 0409089).
157. R.e. Arnowitt Gravitation: An Introduction to Current Research 1962 Wiley New York
158. J. York in: W.H. Zurek (Eds.), Between Quantum and Cosmos 1988 Princeton University Press Princeton 246
159. A.D. Sakharov Vacuum quantum fluctuations in curved space and the theory of gravitation Sov. Phys. Dokl. 12 1968 1040-1041
160. T. Padmanabhan, Gravity as elasticity of spacetime: A paradigm to understand horizon thermodynamics and cosmological constant, Int. J. Mod. Phys. D, in press (gr-qc/0408051).
161. T. Padmanabhan Gravitational entropy of static spacetimes and microscopic density of states Class. Quant. Grav. 21 2004 4485-4494
162. R.C. Tolman On the use of the energy-momentum principle in general relativity Phys. Rev. 35 1930 875-895
163. T. Padmanabhan The holography of gravity encoded in a relation between entropy horizon area and action for gravity, Gen. Rel. Grav. 34 2002 2029-2035 second prize essay, Gravity Research Foundation Essay Contest, 2002
164. T. Padmanabhan Limitations on the operational definition of space-time events and quantum gravity Class. Quant. Grav. 4 1987 L107-L113
165. G. Amelino-Camelia Limits on the measurability of space-time distances in the semiclassical approximation of quantum gravity Mod. Phys. Lett. A 9 1994 3415-3422
166. G. Amelino-Camelia, The three perspectives on the quantum-gravity problem and their implications for the fate of lorentz symmetry, 2003 (gr-qc/0309054).
167. J.D. Bekenstein The quantum mass spectrum of the kerr black hole Lett. Nuovo Cim. 11 1974 467
168. G. Gour Quantum mechanics of a black hole Phys. Rev. D 61 2000 124007
169. J. Louko J. Makela Area spectrum of the schwarzschild black hole Phys. Rev. D 54 1996 4982-4996
170. V.F. Mukhanov Are black holes quantized? JETP Lett. 44 1986 63-66
171. Y.I. Kogan Quantization of the mass of a black hole in string theory JETP Lett. 44 1986 267-270
172. P.O. Mazur Are there topological black hole solitons in string theory? Gen. Re. Grav. 19 1987 1173-1180
173. C.O. Lousto The emergence of an effective two-dimensional quantum description from the study of critical phenomena in black holes Phys. Rev. D 51 1995 1733-1740
174. Y. Peleg The spectrum of quantum dust black holes Phys. Lett. B 356 1995 462-465
175. S. Das P. Ramadevi U.A. Yajnik Black hole area quantization Mod. Phys. Lett. A 17 2002 993-1000
176. U.H. Danielsson M. Schiffer Quantum mechanics, common sense and the black hole information paradox Phys. Rev. D 48 1993 4779-4784
177. M. Maggiore Black holes as quantum membranes Nucl. Phys. B 429 1994 205-228
178. J.D. Bekenstein V.F. Mukhanov Spectroscopy of the quantum black hole Phys. Lett. B 360 1995 7-12
179. H.A. Kastrup On the quantum levels of isolated spherically symmetric gravitational systems Phys. Lett. B 385 1996 75-80