Built on

P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th]
Original
1903
Earlier work this paper cites.
G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox,” arXiv:1905.08255 [hep-th]
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,” JHEP
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, “The Page curve of Hawking radiation from semiclassical geometry,” JHEP
Original
1908
Earlier work this paper cites.
C. Akers, N. Engelhardt, and D. Harlow, “Simple holographic models of black hole evaporation,” arXiv:1910.00972 [hep-th]
Original
1910
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell, and D. Wakeham, “Information radiation in BCFT models of black holes,” JHEP
Original
1910
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. Maldacena, “Islands outside the horizon,” arXiv:1910.11077 [hep-th]
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, “Replica wormholes and the black hole interior,” arXiv:1911.11977 [hep-th]
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation,” JHEP
Original
1911
Earlier work this paper cites.
R. Bousso and M. Tomašević, “Unitarity From a Smooth Horizon?,” arXiv:1911.06305 [hep-th]
Original
1911
Earlier work this paper cites.
H. Z. Chen, Z. Fisher, J. Hernandez, R. C. Myers, and S.-M. Ruan, “Information Flow in Black Hole Evaporation,” JHEP
Original
1911
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. E. Santos, “Entanglement islands in higher dimensions,” arXiv:1911.09666 [hep-th]
Original
1911
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and the second law,” Nuovo Cim. Lett
1972
Earlier work this paper cites.
S. W. Hawking, “Black hole explosions,” Nature
1974
Earlier work this paper cites.
S. W. Hawking, “Black Holes and Thermodynamics,” Phys. Rev. D
1976
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D
1977
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett. B
1983
Earlier work this paper cites.
The University of Chicago Press, Chicago, 1984
R. M. Wald, General Relativity · 1984
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys. B
1985
Earlier work this paper cites.
I. Affleck and A. W. W. Ludwig, “Universal noninteger ‘ground state degeneracy’ in critical quantum systems,” Phys. Rev. Lett
1991
Earlier work this paper cites.

Similar

D. A. Lowe, J. Polchinski, L. Susskind, L. Thorlacius, and J. Uglum, “Black hole complementarity versus locality,” Phys. Rev. D
1995
Cited alongside, same era.
J. Maldacena, “The Large N N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
L. Randall and R. Sundrum, “A large mass hierarchy from a small extra dimension,” Phys. Rev. Lett
1999
Cited alongside, same era.
A. Karch and L. Randall, “Locally localized gravity,” JHEP
2001
Cited alongside, same era.
R. Bousso and L. Randall, “Holographic domains of Anti-de Sitter space,” JHEP
2002
Cited alongside, same era.
T. Hartman, E. Shaghoulian, and A. Strominger, “Islands in Asymptotically Flat 2D Gravity,” arXiv:2004.13857 [hep-th]

Then

V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP
Original
2007
Later among the works it cites.
T. Takayanagi, “Holographic Dual of BCFT,” Phys. Rev. Lett
Original
2011
Later among the works it cites.
M. Fujita, T. Takayanagi, and E. Tonni, “Aspects of AdS/BCFT,” JHEP
Original
2011
Later among the works it cites.
A. Lewkowycz and J. Maldacena, “Generalized gravitational entropy,” JHEP
Original
2013
Later among the works it cites.
T. Faulkner, A. Lewkowycz, and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP
Original

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2020

Gravity/Ensemble Duality

Bousso, Raphael, Wildenhain, Elizabeth

Understand

For the first time, a gravitational calculation was recently shown to yield the Page curve for the entropy of Hawking radiation, consistent with unitary evolution.

However, the calculation takes as essential input Hawking's result that the radiation entropy becomes large at late times.
We call this apparent contradiction the state paradox.
We exhibit its manifestations in standard and doubly-holographic settings, with and without an external bath.

Built on

P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th]
Original
1903
Earlier work this paper cites.
G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox,” arXiv:1905.08255 [hep-th]
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,” JHEP
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, “The Page curve of Hawking radiation from semiclassical geometry,” JHEP
Original
1908
Earlier work this paper cites.
C. Akers, N. Engelhardt, and D. Harlow, “Simple holographic models of black hole evaporation,” arXiv:1910.00972 [hep-th]
Original
1910
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell, and D. Wakeham, “Information radiation in BCFT models of black holes,” JHEP
Original
1910
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. Maldacena, “Islands outside the horizon,” arXiv:1910.11077 [hep-th]
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, “Replica wormholes and the black hole interior,” arXiv:1911.11977 [hep-th]
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation,” JHEP
Original
1911
Earlier work this paper cites.
R. Bousso and M. Tomašević, “Unitarity From a Smooth Horizon?,” arXiv:1911.06305 [hep-th]
Original
1911
Earlier work this paper cites.
H. Z. Chen, Z. Fisher, J. Hernandez, R. C. Myers, and S.-M. Ruan, “Information Flow in Black Hole Evaporation,” JHEP
Original
1911
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. E. Santos, “Entanglement islands in higher dimensions,” arXiv:1911.09666 [hep-th]
Original
1911
Earlier work this paper cites.
J. D. Bekenstein, “Black holes and the second law,” Nuovo Cim. Lett
1972
Earlier work this paper cites.
S. W. Hawking, “Black hole explosions,” Nature
1974
Earlier work this paper cites.
S. W. Hawking, “Black Holes and Thermodynamics,” Phys. Rev. D
1976
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D
1977
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett. B
1983
Earlier work this paper cites.
The University of Chicago Press, Chicago, 1984
R. M. Wald, General Relativity · 1984
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys. B
1985
Earlier work this paper cites.
I. Affleck and A. W. W. Ludwig, “Universal noninteger ‘ground state degeneracy’ in critical quantum systems,” Phys. Rev. Lett
1991
Earlier work this paper cites.

Similar

D. A. Lowe, J. Polchinski, L. Susskind, L. Thorlacius, and J. Uglum, “Black hole complementarity versus locality,” Phys. Rev. D
1995
Cited alongside, same era.
J. Maldacena, “The Large N N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
L. Randall and R. Sundrum, “A large mass hierarchy from a small extra dimension,” Phys. Rev. Lett
1999
Cited alongside, same era.
A. Karch and L. Randall, “Locally localized gravity,” JHEP
2001
Cited alongside, same era.
R. Bousso and L. Randall, “Holographic domains of Anti-de Sitter space,” JHEP
2002
Cited alongside, same era.
T. Hartman, E. Shaghoulian, and A. Strominger, “Islands in Asymptotically Flat 2D Gravity,” arXiv:2004.13857 [hep-th]