Microscopic Origin of the Entropy of Black Holes in General Relativity

Balasubramanian, Vijay; Lawrence, Albion; Magán, Javier M.; Sasieta, Martin

doi:10.1103/PhysRevX.14.011024

Title: Microscopic Origin of the Entropy of Black Holes in General Relativity

Journal Article · 20 February 2024 · Physical Review. X

DOI: https://doi.org/10.1103/PhysRevX.14.011024 · OSTI ID:2310408

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We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity with a negative cosmological constant in any dimension. Wormholes in the Euclidean path integral for gravity cause these states to have small, but nonzero, quantum mechanical overlaps that have a universal form. The overlaps have a dramatic consequence: The microstates span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy. The semiclassical microstates we construct contain Einstein-Rosen bridges of arbitrary size behind their horizons. Our results imply that all these bridges can be interpreted as quantum superpositions of wormholes of size at most exponential in the entropy. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0013528; SC0009986; SC0020360

OSTI ID:: 2310408

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Journal Issue: 1 Vol. 14; ISSN PRXHAE; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (93)

Black Hole Physics: Basic Concepts and New Developments Frolov, Valeri P.; Novikov, Igor D. Fundamental Theories of Physics https://doi.org/10.1007/978-94-011-5139-9	book	January 1998
The holographic Weyl anomaly Henningson, M.; Skenderis, K. Journal of High Energy Physics, Vol. 1998, Issue 07 https://doi.org/10.1088/1126-6708/1998/07/023	journal	July 1998
The Recursion Method: Application to Many-Body Dynamics Viswanath, V. S.; Müller, Gerhard Lecture Notes in Physics Monographs https://doi.org/10.1007/978-3-540-48651-0	book	January 1994
An integrable road to a perturbative plateau Blommaert, Andreas; Kruthoff, Jorrit; Yao, Shunyu Journal of High Energy Physics, Vol. 2023, Issue 4 https://doi.org/10.1007/JHEP04(2023)048	journal	April 2023
Unitarity and the Hilbert space of quantum gravity Hsu, Stephen D. H.; Reeb, David Classical and Quantum Gravity, Vol. 25, Issue 23 https://doi.org/10.1088/0264-9381/25/23/235007	journal	November 2008
Inconsistency of islands in theories with long-range gravity Geng, Hao; Karch, Andreas; Perez-Pardavila, Carlos Journal of High Energy Physics, Vol. 2022, Issue 1 https://doi.org/10.1007/JHEP01(2022)182	journal	January 2022
Black Holes and Entropy Bekenstein, Jacob D. Physical Review D, Vol. 7, Issue 8 https://doi.org/10.1103/PhysRevD.7.2333	journal	April 1973
Eigenstate Thermalization and Disorder Averaging in Gravity Pollack, Jason; Rozali, Moshe; Sully, James Physical Review Letters, Vol. 125, Issue 2 https://doi.org/10.1103/PhysRevLett.125.021601	journal	July 2020
Holographic representation of local bulk operators Hamilton, Alex; Kabat, Daniel; Lifschytz, Gilad Physical Review D, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevD.74.066009	journal	September 2006
Geometry of Krylov complexity Caputa, Pawel; Magan, Javier M.; Patramanis, Dimitrios Physical Review Research, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevResearch.4.013041	journal	January 2022
Particle creation by black holes Hawking, S. W. Communications In Mathematical Physics, Vol. 43, Issue 3 https://doi.org/10.1007/BF02345020	journal	August 1975
Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity Mertens, Thomas G.; Turiaci, Gustavo J. Living Reviews in Relativity, Vol. 26, Issue 1 https://doi.org/10.1007/s41114-023-00046-1	journal	July 2023
Surface terms as counterterms in the AdS-CFT correspondence Emparan, Roberto; Johnson, Clifford V.; Myers, Robert C. Physical Review D, Vol. 60, Issue 10 https://doi.org/10.1103/PhysRevD.60.104001	journal	October 1999
Lecture notes on holographic renormalization Skenderis, Kostas Classical and Quantum Gravity, Vol. 19, Issue 22 https://doi.org/10.1088/0264-9381/19/22/306	journal	November 2002
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
From operator statistics to wormholes Altland, Alexander; Bagrets, Dmitry; Nayak, Pranjal Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033259	journal	September 2021
Late time physics of holographic quantum chaos Altland, Alexander; Sonner, Julian SciPost Physics, Vol. 11, Issue 2 https://doi.org/10.21468/SciPostPhys.11.2.034	journal	January 2021
Entanglement between two gravitating universes Balasubramanian, Vijay; Kar, Arjun; Ugajin, Tomonori Classical and Quantum Gravity, Vol. 39, Issue 17 https://doi.org/10.1088/1361-6382/ac3c8b	journal	August 2022
The large $N$ limit of superconformal field theories and supergravity Maldacena, Juan Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a1	journal	January 1998
A covariant entropy conjecture Bousso, Raphael Journal of High Energy Physics, Vol. 1999, Issue 07 https://doi.org/10.1088/1126-6708/1999/07/004	journal	July 1999
The stretched horizon and black hole complementarity Susskind, Leonard; Thorlacius, Lárus; Uglum, John Physical Review D, Vol. 48, Issue 8 https://doi.org/10.1103/PhysRevD.48.3743	journal	October 1993
Complexity and shock wave geometries Stanford, Douglas; Susskind, Leonard Physical Review D, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevD.90.126007	journal	December 2014
Quantum source of entropy for black holes Bombelli, Luca; Koul, Rabinder K.; Lee, Joohan Physical Review D, Vol. 34, Issue 2 https://doi.org/10.1103/PhysRevD.34.373	journal	July 1986
Quantum statistical mechanics in a closed system Deutsch, J. M. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.2046	journal	February 1991
No ensemble averaging below the black hole threshold Schlenker, Jean-Marc; Witten, Edward Journal of High Energy Physics, Vol. 2022, Issue 7 https://doi.org/10.1007/JHEP07(2022)143	journal	July 2022
The volume of the black hole interior at late times Iliesiu, Luca V.; Mezei, Márk; Sárosi, Gábor Journal of High Energy Physics, Vol. 2022, Issue 7 https://doi.org/10.1007/JHEP07(2022)073	journal	July 2022
The Oxford Handbook of Random Matrix Theory Akemann, Gernot; Baik, Jinho; Di Francesco, Philippe https://doi.org/10.1093/oxfordhb/9780198744191.001.0001	book	September 2015
Tridiagonalizing random matrices Balasubramanian, Vijay; Magan, Javier M.; Wu, Qingyue Physical Review D, Vol. 107, Issue 12 https://doi.org/10.1103/PhysRevD.107.126001	journal	June 2023
Black holes, complexity and quantum chaos Magán, Javier M. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)043	journal	September 2018
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)090	journal	August 2013
Local Operators in the Eternal Black Hole Papadodimas, Kyriakos; Raju, Suvrat Physical Review Letters, Vol. 115, Issue 21 https://doi.org/10.1103/PhysRevLett.115.211601	journal	November 2015
Interacting systems and wormholes Betzios, P.; Kiritsis, E.; Papadoulaki, O. Journal of High Energy Physics, Vol. 2022, Issue 2 https://doi.org/10.1007/JHEP02(2022)126	journal	February 2022
AdS$_{2}$ holography and the SYK model Sarosi, Gabor Proceedings of XIII Modave Summer School in Mathematical Physics — PoS(Modave2017) https://doi.org/10.22323/1.323.0001	conference	March 2018
Renormalization of entanglement entropy and the gravitational effective action Cooperman, Joshua H.; Luty, Markus A. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)045	journal	December 2014
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/JHEP12(2019)063	journal	December 2019
The Library of Babel Balasubramanian, Vijay; Jejjala, Vishnu; SimÓN, Joan International Journal of Modern Physics D, Vol. 14, Issue 12 https://doi.org/10.1142/S0218271805007826	journal	December 2005
Erratum to: Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)002	journal	September 2018
Singular hypersurfaces and thin shells in general relativity Israel, W. Il Nuovo Cimento B Series 10, Vol. 48, Issue 2 https://doi.org/10.1007/BF02712210	journal	April 1967
The entropy of Hawking radiation Almheiri, Ahmed; Hartman, Thomas; Maldacena, Juan Reviews of Modern Physics, Vol. 93, Issue 3 https://doi.org/10.1103/RevModPhys.93.035002	journal	July 2021
The statistical mechanics of near-extremal black holes Iliesiu, Luca V.; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2021, Issue 5 https://doi.org/10.1007/JHEP05(2021)145	journal	May 2021
Scrambling the spectral form factor: Unitarity constraints and exact results del Campo, A.; Molina-Vilaplana, J.; Sonner, J. Physical Review D, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevD.95.126008	journal	June 2017
Quantum error correction in the black hole interior Balasubramanian, Vijay; Kar, Arjun; Li, Cathy Journal of High Energy Physics, Vol. 2023, Issue 7 https://doi.org/10.1007/JHEP07(2023)189	journal	July 2023
Wormholes from heavy operator statistics in AdS/CFT Sasieta, Martin Journal of High Energy Physics, Vol. 2023, Issue 3 https://doi.org/10.1007/JHEP03(2023)158	journal	March 2023
Information in black hole radiation Page, Don N. Physical Review Letters, Vol. 71, Issue 23 https://doi.org/10.1103/PhysRevLett.71.3743	journal	December 1993
Non-isometric quantum error correction in gravity Kar, Arjun Journal of High Energy Physics, Vol. 2023, Issue 2 https://doi.org/10.1007/JHEP02(2023)195	journal	February 2023
Averaging over Narain moduli space Maloney, Alexander; Witten, Edward Journal of High Energy Physics, Vol. 2020, Issue 10 https://doi.org/10.1007/JHEP10(2020)187	journal	October 2020
The ghost in the radiation: robust encodings of the black hole interior Kim, Isaac; Tang, Eugene; Preskill, John Journal of High Energy Physics, Vol. 2020, Issue 6 https://doi.org/10.1007/JHEP06(2020)031	journal	June 2020
A Stress Tensor for Anti-de Sitter Gravity Balasubramanian, Vijay; Kraus, Per Communications in Mathematical Physics, Vol. 208, Issue 2 https://doi.org/10.1007/s002200050764	journal	December 1999
Quantum complexity of time evolution with chaotic Hamiltonians Balasubramanian, Vijay; DeCross, Matthew; Kar, Arjun Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/JHEP01(2020)134	journal	January 2020
Three approaches to the quantitative definition of information ^* Kolmogorov, A. N. International Journal of Computer Mathematics, Vol. 2, Issue 1-4 https://doi.org/10.1080/00207166808803030	journal	January 1968
What do CFTs tell us about anti-de Sitter spacetimes? Balasubramanian, Vijay; Giddings, Steven B.; Lawrence, Albion Journal of High Energy Physics, Vol. 1999, Issue 03 https://doi.org/10.1088/1126-6708/1999/03/001	journal	March 1999
The Page curve of Hawking radiation from semiclassical geometry Almheiri, Ahmed; Mahajan, Raghu; Maldacena, Juan Journal of High Energy Physics, Vol. 2020, Issue 3 https://doi.org/10.1007/JHEP03(2020)149	journal	March 2020
Spin structures and baby universes Balasubramanian, Vijay; Kar, Arjun; Ross, Simon F. Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)192	journal	September 2020
Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information Marolf, Donald; Maxfield, Henry Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)044	journal	August 2020
Fermionic localization of the schwarzian theory Stanford, Douglas; Witten, Edward Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)008	journal	October 2017
Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT Fu, Zicao; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/JHEP11(2019)040	journal	November 2019
The library of Babel: on the origin of gravitational thermodynamics Balasubramanian, Vijay; Boer, Jan de; Jejjala, Vishnu Journal of High Energy Physics, Vol. 2005, Issue 12 https://doi.org/10.1088/1126-6708/2005/12/006	journal	December 2005
Random-matrix theories in quantum physics: common concepts Guhr, Thomas; Müller–Groeling, Axel; Weidenmüller, Hans A. Physics Reports, Vol. 299, Issue 4-6 https://doi.org/10.1016/S0370-1573(97)00088-4	journal	June 1998
Anti de Sitter space and holography Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a2	journal	January 1998
On operator growth and emergent Poincaré symmetries Magán, Javier M.; Simón, Joan Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)071	journal	May 2020
Overcounting of interior excitations: a resolution to the bags of gold paradox in AdS Chakravarty, Joydeep Journal of High Energy Physics, Vol. 2021, Issue 2 https://doi.org/10.1007/JHEP02(2021)027	journal	February 2021
Black hole entanglement entropy and the renormalization group Jacobson, Ted; Satz, Alejandro Physical Review D, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevD.87.084047	journal	April 2013
Semiclassical 3D gravity as an average of large-c CFTs Chandra, Jeevan; Collier, Scott; Hartman, Thomas Journal of High Energy Physics, Vol. 2022, Issue 12 https://doi.org/10.1007/JHEP12(2022)069	journal	December 2022
AdS3 gravity and random CFT Cotler, Jordan; Jensen, Kristan Journal of High Energy Physics, Vol. 2021, Issue 4 https://doi.org/10.1007/JHEP04(2021)033	journal	April 2021
Computational complexity and black hole horizons: Computational complexity and black hole horizons Susskind, Leonard Fortschritte der Physik, Vol. 64, Issue 1 https://doi.org/10.1002/prop.201500092	journal	January 2016
On the quantum structure of a black hole 't Hooft, Gerard Nuclear Physics B, Vol. 256 https://doi.org/10.1016/0550-3213(85)90418-3	journal	January 1985
A Universal Operator Growth Hypothesis Parker, Daniel E.; Cao, Xiangyu; Avdoshkin, Alexander Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041017	journal	October 2019
Geometric secret sharing in a model of Hawking radiation Balasubramanian, Vijay; Kar, Arjun; Parrikar, Onkar Journal of High Energy Physics, Vol. 2021, Issue 1 https://doi.org/10.1007/JHEP01(2021)177	journal	January 2021
Replica wormholes and the black hole interior Penington, Geoff; Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2022, Issue 3 https://doi.org/10.1007/JHEP03(2022)205	journal	March 2022
Expanding the black hole interior: partially entangled thermal states in SYK Goel, Akash; Lam, Ho Tat; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)156	journal	February 2019
Eternal black holes in anti-de Sitter Maldacena, Juan Journal of High Energy Physics, Vol. 2003, Issue 04 https://doi.org/10.1088/1126-6708/2003/04/021	journal	April 2003
Addendum to computational complexity and black hole horizons: Addendum to computational complexity and black hole horizons Susskind, Leonard Fortschritte der Physik, Vol. 64, Issue 1 https://doi.org/10.1002/prop.201500093	journal	January 2016
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)106	journal	August 2016
Replica wormholes and the entropy of Hawking radiation Almheiri, Ahmed; Hartman, Thomas; Maldacena, Juan Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)013	journal	May 2020
Large N algebras and generalized entropy Chandrasekaran, Venkatesa; Penington, Geoff; Witten, Edward Journal of High Energy Physics, Vol. 2023, Issue 4 https://doi.org/10.1007/JHEP04(2023)009	journal	April 2023
Entropy and area Srednicki, Mark Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevLett.71.666	journal	August 1993
The world as a hologram Susskind, Leonard Journal of Mathematical Physics, Vol. 36, Issue 11 https://doi.org/10.1063/1.531249	journal	November 1995
Holographic probes of anti–de Sitter spacetimes Balasubramanian, Vijay; Kraus, Per; Lawrence, Albion Physical Review D, Vol. 59, Issue 10 https://doi.org/10.1103/PhysRevD.59.104021	journal	April 1999
The Python’s Lunch: geometric obstructions to decoding Hawking radiation Brown, Adam R.; Gharibyan, Hrant; Penington, Geoff Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)121	journal	August 2020
Planar perturbation expansion Cvitanović, Predrag Physics Letters B, Vol. 99, Issue 1 https://doi.org/10.1016/0370-2693(81)90801-7	journal	February 1981
Singular hypersurfaces and thin shells in general relativity Israel, W. Il Nuovo Cimento B Series 10, Vol. 44, Issue 1 https://doi.org/10.1007/BF02710419	journal	July 1966
Entanglement wedge reconstruction and the information paradox Penington, Geoffrey Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)002	journal	September 2020
Microscopic origin of the Bekenstein-Hawking entropy Strominger, Andrew; Vafa, Cumrun Physics Letters B, Vol. 379, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00345-0	journal	June 1996
Matrix Models for Eigenstate Thermalization Jafferis, Daniel Louis; Kolchmeyer, David K.; Mukhametzhanov, Baur Physical Review X, Vol. 13, Issue 3 https://doi.org/10.1103/PhysRevX.13.031033	journal	September 2023
Gauge theory correlators from non-critical string theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. Physics Letters B, Vol. 428, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00377-3	journal	May 1998
Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)118	journal	May 2017
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Average entropy of a subsystem Page, Don N. Physical Review Letters, Vol. 71, Issue 9 https://doi.org/10.1103/PhysRevLett.71.1291	journal	August 1993
A violation of global symmetries from replica wormholes and the fate of black hole remnants Hsin, Po-Shen; Iliesiu, Luca V.; Yang, Zhenbin Classical and Quantum Gravity, Vol. 38, Issue 19 https://doi.org/10.1088/1361-6382/ac2134	journal	September 2021
Particle creation by black holes Hawking, S. W. Communications in Mathematical Physics, Vol. 46, Issue 2 https://doi.org/10.1007/BF01608497	journal	June 1976
Quantum chaos and the complexity of spread of states Balasubramanian, Vijay; Caputa, Pawel; Magan, Javier M. Physical Review D, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevD.106.046007	journal	August 2022
Random statistics of OPE coefficients and Euclidean wormholes Belin, Alexandre; de Boer, Jan Classical and Quantum Gravity, Vol. 38, Issue 16 https://doi.org/10.1088/1361-6382/ac1082	journal	July 2021
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Lanczos, C. Journal of Research of the National Bureau of Standards, Vol. 45, Issue 4 https://doi.org/10.6028/jres.045.026	journal	October 1950

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