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Title: Gravity/ensemble duality

Abstract

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. We clarify which version(s) of the Ryu-Takayanagi prescription apply in each setting. We show that the two possible homology rules in the presence of a braneworld generate a bulk dual of the state paradox. The paradox is resolved if the gravitational path integral computes averaged quantities in a suitable ensemble of unitary theories, a possibility supported independently by several recent developments.

Authors:
; ORCiD logo
Publication Date:
Research Org.:
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1661729
Alternate Identifier(s):
OSTI ID: 1713181; OSTI ID: 1756381
Grant/Contract Number:  
SC0019380; AC02-05CH11231; PHY1820912
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 6; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; gauge-gravity dualities; general relativity; quantum aspects of black holes; quantum gravity

Citation Formats

Bousso, Raphael, and Wildenhain, Elizabeth. Gravity/ensemble duality. United States: N. p., 2020. Web. https://doi.org/10.1103/PhysRevD.102.066005.
Bousso, Raphael, & Wildenhain, Elizabeth. Gravity/ensemble duality. United States. https://doi.org/10.1103/PhysRevD.102.066005
Bousso, Raphael, and Wildenhain, Elizabeth. Wed . "Gravity/ensemble duality". United States. https://doi.org/10.1103/PhysRevD.102.066005.
@article{osti_1661729,
title = {Gravity/ensemble duality},
author = {Bousso, Raphael and Wildenhain, Elizabeth},
abstractNote = {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. We clarify which version(s) of the Ryu-Takayanagi prescription apply in each setting. We show that the two possible homology rules in the presence of a braneworld generate a bulk dual of the state paradox. The paradox is resolved if the gravitational path integral computes averaged quantities in a suitable ensemble of unitary theories, a possibility supported independently by several recent developments.},
doi = {10.1103/PhysRevD.102.066005},
journal = {Physical Review D},
number = 6,
volume = 102,
place = {United States},
year = {2020},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.102.066005

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Works referenced in this record:

The Page curve of Hawking radiation from semiclassical geometry
journal, March 2020

  • Almheiri, Ahmed; Mahajan, Raghu; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2020, Issue 3
  • DOI: 10.1007/JHEP03(2020)149

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015


Violations of the Equivalence Principle by a Nonlocally Reconstructed Vacuum at the Black Hole Horizon
journal, January 2014


Holographic representation of local bulk operators
journal, September 2006


Large Mass Hierarchy from a Small Extra Dimension
journal, October 1999


Black hole entropy as entanglement entropy: a holographic derivation
journal, June 2006


Gauge-Gravity Duality and the Black Hole Interior
journal, October 2013


Replica wormholes and the entropy of Hawking radiation
journal, May 2020

  • Almheiri, Ahmed; Hartman, Thomas; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)013

Lower dimensional gravity
journal, January 1985


Black holes and the second law
journal, August 1972

  • Bekenstein, J. D.
  • Lettere Al Nuovo Cimento Series 2, Vol. 4, Issue 15
  • DOI: 10.1007/BF02757029

On spacetime entanglement
journal, June 2013

  • Myers, Robert C.; Pourhasan, Razieh; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)013

Black hole explosions?
journal, March 1974


Islands in asymptotically flat 2D gravity
journal, July 2020

  • Hartman, Thomas; Shaghoulian, Edgar; Strominger, Andrew
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)022

An apologia for firewalls
journal, September 2013

  • Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2013, Issue 9
  • DOI: 10.1007/JHEP09(2013)018

Black holes: complementarity or firewalls?
journal, February 2013

  • Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)062

The Black Hole Information Problem
conference, January 2017

  • Polchinski, Joseph
  • 2015 Theoretical Advanced Study Institute in Elementary Particle Physics, New Frontiers in Fields and Strings
  • DOI: 10.1142/9789813149441_0006

Holographic Domains of Anti-de Sitter Space
journal, April 2002


Black holes and thermodynamics
journal, January 1976


Gravitation and hamiltonian structure in two spacetime dimensions
journal, June 1983


Holographic proof of the quantum null energy condition
journal, July 2016


Firewalls from double purity
journal, October 2013


Action integrals and partition functions in quantum gravity
journal, May 1977


Extremal surface barriers
journal, March 2014


Page curve for an evaporating black hole
journal, May 2020

  • Gautason, Friðrik Freyr; Schneiderbauer, Lukas; Sybesma, Watse
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)091

Simple holographic models of black hole evaporation
journal, August 2020

  • Akers, Chris; Engelhardt, Netta; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2020, Issue 8
  • DOI: 10.1007/JHEP08(2020)032

Locally localized gravity
journal, May 2001


Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006


The large $N$ limit of superconformal field theories and supergravity
journal, January 1998


The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
journal, December 2019

  • Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald
  • Journal of High Energy Physics, Vol. 2019, Issue 12
  • DOI: 10.1007/JHEP12(2019)063

Holographic Dual of a Boundary Conformal Field Theory
journal, August 2011


Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

  • Almheiri, Ahmed; Dong, Xi; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)163

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014


Information flow in black hole evaporation
journal, March 2020

  • Chen, Hong Zhe; Fisher, Zachary; Hernandez, Juan
  • Journal of High Energy Physics, Vol. 2020, Issue 3
  • DOI: 10.1007/JHEP03(2020)152

Universal noninteger ‘‘ground-state degeneracy’’ in critical quantum systems
journal, July 1991


Information radiation in BCFT models of black holes
journal, May 2020

  • Rozali, Moshe; Sully, James; Van Raamsdonk, Mark
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)004

A covariant holographic entanglement entropy proposal
journal, July 2007

  • Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2007, Issue 07
  • DOI: 10.1088/1126-6708/2007/07/062

Generalized gravitational entropy
journal, August 2013

  • Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)090

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
journal, July 2016


Black hole complementarity versus locality
journal, December 1995

  • Lowe, David A.; Polchinski, Joseph; Susskind, Leonard
  • Physical Review D, Vol. 52, Issue 12
  • DOI: 10.1103/PhysRevD.52.6997

Complementarity is not enough
journal, June 2013


Black hole microstate cosmology
journal, July 2019

  • Cooper, Sean; Rozali, Moshe; Swingle, Brian
  • Journal of High Energy Physics, Vol. 2019, Issue 7
  • DOI: 10.1007/JHEP07(2019)065

Aspects of AdS/BCFT
journal, November 2011

  • Fujita, Mitsutoshi; Takayanagi, Tadashi; Tonni, Erik
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)043

Aspects of holographic entanglement entropy
journal, August 2006


Entanglement islands in higher dimensions
journal, January 2020


Jerusalem lectures on black holes and quantum information
journal, February 2016


Quantum corrections to holographic entanglement entropy
journal, November 2013

  • Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)074

Relative entropy equals bulk relative entropy
journal, June 2016

  • Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)004