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The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity.
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98
1936
Earlier work this paper cites.
J. S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82
1951
Earlier work this paper cites.
R. Kubo, Statistical mechanical theory of irreversible processes, J. Phys. Soc. Japan 12
1957
Earlier work this paper cites.
N. N. Bogoliubov, Sov. Phys. JETP 7
1958
Earlier work this paper cites.
P. C. Martin and J. S. Schwinger, Theory of many particle systems, Phys. Rev. 115
1959
Earlier work this paper cites.
J. Goldstone, A. Salam, and S. Weinberg, Broken symmetries, Phys. Rev. 127
1962
Earlier work this paper cites.
R. P. Feynman and A. R. Hibbs, emphQuantum mechanics and path integrals (McGraw-Hill, New York, 1965)
1965
Earlier work this paper cites.
R. Haag, N. M. Hugenholtz, and M. Winnink, On the equilibrium states in quantum statistical mechanics, Commun. Math. Phys. 5
1967
Earlier work this paper cites.
D. Lynden-Bell and R. Wood, The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems, Mon. Not. R. astr. Soc. 138
1968
Earlier work this paper cites.
L. Parker, Quantized fields and particle creation in expanding universes, Phys. Rev. 183
1969
Earlier work this paper cites.
J. D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
S. W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25
1972
Earlier work this paper cites.
Ya. B. Zel’dovich and A. A. Starobinsky, Particle production and vacuum polarization in an anisotropic gravitational field, Zh. Eksp. Teor. Fiz. 61
1972
Earlier work this paper cites.
J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7
1973
Earlier work this paper cites.
J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973)
1973
Earlier work this paper cites.
S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time (Cambridge University Press, Cambridge, 1973)
1973
Earlier work this paper cites.
S. W. Hawking, Black hole explosions, Nature 248
1974
Earlier work this paper cites.
C. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88
1974
Earlier work this paper cites.
S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43
1975
Earlier work this paper cites.
R. M. Wald, On particle creation by black holes, Commun. Math. Phys. . 45
1975
Earlier work this paper cites.
L. Parker, Probability distribution of particles created by a black hole, Phys. Rev. D 12
1975
Earlier work this paper cites.
D. N. Page, Particle emission rates from a black hole: massless articles from an uncharged, nonrotating hole, Phys. Rev. D 13
1976
Earlier work this paper cites.
W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14
1976
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, Path integral derivation of black hole radiance, Phys. Rev. D 13
1976
Earlier work this paper cites.
J. J. Bisognano and E. H. Wichmann, On the duality condition for quantum fields, J. Math. Phys. 17
1976
Earlier work this paper cites.
T. Damour and R. Ruffini, Black hole evaporation in the Klein-Sauter-Heisenberg-Euler formalism, Phys. Rev. D 14
1976
Earlier work this paper cites.
P. C. W./ Davies, S. A./ Fulling, and W. G./ Unruh, Energy-momentum tensor near an evaporating black hole, Phys. Rev. D 13
1976
Earlier work this paper cites.
G. W. Gibbons and M J. Perry, Black holes in thermal equilibrium, Phys. Rev. Lett. 36
1976
Earlier work this paper cites.
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57
1976
Earlier work this paper cites.
S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14
1976
Earlier work this paper cites.
G. W. Gibbons and S. W, Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15
1977
Earlier work this paper cites.
P. C. W. Davies, The thermodynamic theory of black holes, Proc. R. Soc. Lond. A . 353
1977
Earlier work this paper cites.
G. W. Gibbons and M. J. Perry, Black holes and thermal Green’s functions, Proc. Roy. Soc. Lond. A 358
1978
Earlier work this paper cites.
B. S. DeWitt, Quantum gravity: the new synthesis, in eds. S. W. Hawking and W. Israel, General relativity: an Einstein centenary survey , (Cambridge University Press, Cambridge, 1979)
1979
Earlier work this paper cites.
W. G. Unruh, Experimental black hole evaporation, Phys. Rev. Lett. 46
1981
Earlier work this paper cites.
V. P. Frolov and G. A. Vilkovisky, Spherically symmetric collapse in quantum gravity, Phys. Lett.— B 106
1981
Earlier work this paper cites.
N. D. Birrell and P. C. W. Davies, Quantum fields in curved space (Cambridge University Press, Cambridge, 1982)
1982
Earlier work this paper cites.
W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature 299
1982
Earlier work this paper cites.
J. W. York, Dynamical origin of black hole radiance, Phys. Rev. D 28
1983
Earlier work this paper cites.
S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. . 87
1983
Earlier work this paper cites.
1983
Earlier work this paper cites.
S. L. Adler, Einstein gravity as a symmetry breaking effect in quantum field theory, Rev. Mod. Phys. 54
1983
Earlier work this paper cites.
M. Henneaux and C. Teitelboim, The cosmological constant as a canonical variable, Phys. Lett. B 143
1984
Earlier work this paper cites.
T. Banks, L. Susskind, and M. E. Peskin, Difficulties for the evolution of pure states Into mixed states, Nucl. Phys. B 244
1984
Earlier work this paper cites.
K. Freese and C. T. Hill, Covariant functional Schrödinger formalism and application to the Hawking effect, Nucl. Phys. B 255
1985
Earlier work this paper cites.
G. ’t Hooft, On the quantum structure of a black hole, Nucl. Phys. B256
1985
Earlier work this paper cites.
W. H. Zurek and K. S. Thorne, Statistical mechanical origin of the entropy of a rotating, charged black hole, Phys. Rev. Lett. 54
1985
Earlier work this paper cites.
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
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, A quantum source of entropy for black holes, Phys. Rev. D . 34
1986
Earlier work this paper cites.
J. l. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270
1986
Earlier work this paper cites.
H. W. J. Blöte, J. A. Cardy, and M. P. Nightingale, Conformal invariance, the central charge, and universal finite size amplitudes at criticality, Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
K. S. Thorne, R H. Price, and D. A. Macdonald, Black holes: the membrane paradigm (Yale University Press, New Haven, 1986)
1986
Earlier work this paper cites.
L. Bombelli, J. Lee, D. Meyer, and R. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
Y. Aharonov, A. Casher, and S. Nussinov, The unitarity puzzle and Planck mass stable particles, Phys. Lett. B 191
1987
Earlier work this paper cites.
R. D. Carlitz and R. S. Willey, The lifetime of a black hole, Phys. Rev. D 36
1987
Earlier work this paper cites.
E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121
1989
Earlier work this paper cites.
W. A. Hiscock and L. D. Weems, Evolution of charged evaporating black holes, Phys. Rev. D 41
1990
Earlier work this paper cites.
S. W. Hawking, Baby universes, Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
T. Jacobson, Black hole evaporation and ultrashort distances, Phys. Rev. D 44
1991
Earlier work this paper cites.
B. S. Kay and R. M. Wald, Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on space-times with a bifurcate Killing horizon, Phys. Rept. 207
1991
Earlier work this paper cites.
M. Banados, C. Teitelboim, and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
R. M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48
1993
Earlier work this paper cites.
M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48
1993
Earlier work this paper cites.
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
V. Frolov and I. Novikov, Dynamical origin of the entropy of a black hole, Phys. Rev. D 48
1993
Earlier work this paper cites.
C. G. Torre and I. M. Anderson, Symmetries of the Einstein equations, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
G. ’t Hooft, Dimensional reduction in quantum gravity, in eds. A. Ali, J. Ellis, and S. Randjbar-Daemi, Salamfestschrift: a collection of talks (World Scientific, Singapore, 1993), arXiv:gr-qc/9310026
1993
Earlier work this paper cites.
L. Susskind, L. Thorlacius, and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48
1993
Earlier work this paper cites.
M. Bañados, C. Teitelboim, and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem, Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
D. Garfinkle, S. B. Giddings, and A. Strominger, Entropy in black hole pair production, Phys. Rev. D 49
1994
Earlier work this paper cites.
F. Dowker, J. P. Gauntlett, D. A. Kastor, and J. H. Traschen, Pair creation of dilaton black holes, Phys. Rev. D 49
1994
Earlier work this paper cites.
R. M. Wald, Quantum field theory in curved spacetime and black hole thermodynamics (University of Chicago Press, Chicago, 1994)
1994
Earlier work this paper cites.
T. Jacobson, A note on Hartle-Hawking vacua, Phys. Rev. D 50
1994
Cited alongside, same era.
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D50
1994
Cited alongside, same era.
S. B. Giddings, Constraints on black hole remnants, Phys. Rev. D 49
1994
Cited alongside, same era.
C. Teitelboim, Action and entropy of extreme and nonextreme black holes, Phys. Rev. D 51
1995
Cited alongside, same era.
S. Carlip and C. Teitelboim, The off-shell black hole, Class. Quant. Grav. 12
1995
Cited alongside, same era.
J. D. Brown, Black hole pair creation and the entropy factor, Phys. Rev. D 51
1995
Cited alongside, same era.
E. Poisson, A relativist’s toolkit (Cambridge University Press, Cambridge, 2004)
2004
Later among the works it cites.
A. Ashtekar and B. Krishnan, Isolated and dynamical horizons and their applications, Living Rev. Rel. 7
2004
Later among the works it cites.
D. N. Page, Hawking radiation and black hole thermodynamics, New J. Phys. 7
2005
Later among the works it cites.
W. G. Unruh and R. Schutzhold, On the universality of the Hawking effect, Phys. Rev. D 71
2005
Later among the works it cites.
S. P. Robinson and F. Wilczek, A relationship between Hawking radiation and gravitational anomalies, Phys. Rev. Lett. 95
2005
Later among the works it cites.
S. Carlip, Conformal field theory, (2+1)-dimensional gravity, and the BTZ black hole, Class. Quantum Grav. 22
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R. B. Mann and S. F. Ross, Cosmological production of charged black hole pairs, Phys. Rev. D 52
1995
Cited alongside, same era.
S. Carlip, The (2+1)-dimensional black hole, Class. Quantum Grav. 12
1995
Cited alongside, same era.
L. Susskind, The world as a hologram, J. Math. Phys. 36
1995
Cited alongside, same era.
W. G. Unruh and R. M. Wald, On evolution laws taking pure states to mixed states in quantum field theory, Phys. Rev. D 52
1995
Cited alongside, same era.
S. B. Giddings, Quantum mechanics of black holes, in eds. E. Gava, A. Masiero, K. S. Narain, S. Randjbar-Daemi, and Q. Shafi, Summer school in high energy physics and cosmology: proceedings (World Scientific, Singapore, 1995), arXiv:hep-th/9412138
1995
Cited alongside, same era.
T. Jacobson, On the origin of the outgoing black hole modes, Phys. Rev. D 53
1996
Cited alongside, same era.
2005
Later among the works it cites.
S. D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53
2005
Later among the works it cites.
A. Ashtekar, J. Engle, and C. Van Den Broeck, Quantum horizons and black hole entropy: Inclusion of distortion and rotation, Class. Quantum Grav. 22
2005
Later among the works it cites.
A. Ghosh and P. Mitra, A bound on the log correction to the black hole area law, Phys. Rev. D 71
2005
Later among the works it cites.
H. E. Camblong and C. R. Ordóñez, Black hole thermodynamics from near-horizon conformal quantum mechanics, Phys. Rev. D 71
2005
Later among the works it cites.
S. Carlip, Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity, Class. Quantum Grav. 22
2005
Later among the works it cites.
I. Booth, Black hole boundaries, Can. J. Phys. 83
2005
Later among the works it cites.
R. Kerner and R. B. Mann, Tunneling, temperature, and Taub-NUT black holes, Phys. Rev. D 73
2006
Later among the works it cites.
S. Iso, H. Umetsu, and F. Wilczek, Hawking radiation from charged black holes via gauge and gravitational anomalies, Phys. Rev. Lett. 96
2006
Later among the works it cites.
S. Iso, H. Umetsu, and F. Wilczek, Anomalies, Hawking radiations and regularity in rotating black holes, Phys. Rev. D 74
2006
Later among the works it cites.
Y. Sekiwa, Thermodynamics of de Sitter black holes: thermal cosmological constant, Phys. Rev. D 73
2006
Later among the works it cites.
S. L. Dubovsky and S. M. Sibiryakov, Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind, Phys. Lett. B . 638
2006
Later among the works it cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96
2006
Later among the works it cites.
R. Emparan, Black hole entropy as entanglement entropy: a holographic derivation, JHEP . 012
2006
Later among the works it cites.
S. D. Mathur, The quantum structure of black holes, Class. Quantum Grav. 23
2006
Later among the works it cites.
E R. Livine and D. R. Terno, Quantum black holes: entropy and entanglement on the horizon Nucl. Phys. B 741
2006
Later among the works it cites.
D. Rideout and S. Zohren, Evidence for an entropy bound from fundamentally discrete gravity, Class. Quantum Grav. 23
2006
Later among the works it cites.
S. A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96
2006
Later among the works it cites.
D. Yang, A simple proof of monogamy of entanglement, Phys. Lett.— A 360
2006
Later among the works it cites.
2007
Later among the works it cites.
C. Eling, B. Z. Foster, T. Jacobson, and A. C. Wall, Lorentz violation and perpetual motion, Phys. Rev. D . 75
2007
Later among the works it cites.
2007
Later among the works it cites.
A. Corichi, J. Diaz-Polo, and E. Fernandez-Borja, Black hole entropy quantization, Phys. Rev. Lett. 98
2007
Later among the works it cites.
T. Jacobson, Renormalization and black hole entropy in loop quantum gravity, Class. Quantum Grav. 24
2007
Later among the works it cites.
S. Iso, T. Morita, and H. Umetsu, Hawking radiation via higher-spin gauge anomalies, Phys. Rev. D 77
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
B. D. Chowdhury and S. D. Mathur, Radiation from the non-extremal fuzzball, Class. Quantum Grav. 25
2008
Later among the works it cites.
S. D. H. Hsu and D. Reeb, Black hole entropy, curved space and monsters, Phys. Lett. B 658
2008
Later among the works it cites.
A. C. Wall, Ten proofs of the generalized second law, J HEP 0906
2009
Later among the works it cites.
S. Carlip, Black hole thermodynamics and statistical mechanics, Lect. Notes Phys. 769
2009
Later among the works it cites.
B. Schutz, A first course in general relativity , 2nd edition (Cambridge University Press, Cambridge, 2009), chap. 11.5
2009
Later among the works it cites.
2009
Later among the works it cites.
2009
Later among the works it cites.
G. Siopsis, Analytic calculation of quasi-normal modes, Lect. Notes Phys. 769
2009
Later among the works it cites.
A. J. M. Medved, On the ‘universal’ quantum area spectrum, Mod. Phys. Lett. A 24
2009
Later among the works it cites.
M. Guica, T. Hartman, W. Song, and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80
2009
Later among the works it cites.
S. D. Mathur, The information paradox: a pedagogical introduction, Class. Quantum Grav. 26
2009
Later among the works it cites.
2010
Later among the works it cites.
2011
Later among the works it cites.
C. Barcelo, S. Liberati, and M. Visser, Analogue gravity, Living Rev. Rel. 14
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
B. P. Dolan, The cosmological constant and the black hole equation of state, Class. Quantum Grav. 28
2011
Later among the works it cites.
A. Ghosh and A. Perez, Black hole entropy and isolated horizons thermodynamics, Phys. Rev. Lett. 27
2011
Later among the works it cites.
J. Engle, K. Noui, A. Perez, and D. Pranzetti, The SU(2) black hole entropy revisited, JHEP 1105
2011
Later among the works it cites.
S. Carlip, Effective conformal descriptions of black hole entropy, Entropy 13
2011
Later among the works it cites.
2011
Later among the works it cites.
S. Carlip, Extremal and nonextremal Kerr/CFT correspondences, JHEP 1104
2012
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
Y. Neiman, The imaginary part of the gravity action and black hole entropy, JHEP 1304
2013
Later among the works it cites.
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 1308
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
K. Papadodimas and S. Raju, The unreasonable effectiveness of exponentially suppressed corrections in preserving information, Int. J. Mod. Phys. D 22
2013
Later among the works it cites.
T. Jacobson, Boundary unitarity and the black hole information paradox, nt. J. Mod. Phys. D 22
2013
Later among the works it cites.
2013
Later among the works it cites.
2014
Closest in time.
A. Almheiri and J. Sully, An uneventful horizon in two dimensions, JHEP 1402
2014
Closest in time.
E. Bianchi, talk at Peyresq Physics 11, June 2014
2014
Closest in time.
2014
Closest in time.
S. Carlip, Four-dimensional entropy from three-dimensional gravity, Phys. Rev. Lett. 115
2015
Closest in time.
S. D. Mathur, What exactly is the information paradox?, Lect. Notes Phys. 769
2030
Closest in time.
S. M. Christensen and S. A. Fulling, Trace Anomalies and the Hawking Effect, Phys. Rev. D 15
2088
Closest in time.
J. W. York, Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev. D 33
2099
Closest in time.