Papers
Topics
Authors
Recent
Search
2000 character limit reached

Microscopic origin of the entropy of black holes in general relativity

Published 5 Dec 2022 in hep-th and gr-qc | (2212.02447v4)

Abstract: We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity with negative cosmological constant in any dimension. Wormholes in the Euclidean path integral for gravity cause these states to have small, but non-zero, 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.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (113)
  1. J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7 (Apr, 1973) 2333–2346. https://link.aps.org/doi/10.1103/PhysRevD.7.2333.
  2. S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys. 43 (1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)].
  3. Springer US, Boston, MA, 1979. https://doi.org/10.1007/978-1-4613-2955-8_4.
  4. J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231–252, arXiv:hep-th/9711200.
  5. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2 (1998) 253–291, arXiv:hep-th/9802150.
  6. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428 (1998) 105–114, arXiv:hep-th/9802109.
  7. S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96 (2006) 181602, arXiv:hep-th/0603001.
  8. A. Lewkowycz and J. Maldacena, “Generalized gravitational entropy,” JHEP 08 (2013) 090, arXiv:1304.4926 [hep-th].
  9. A. Strominger and C. Vafa, “Microscopic origin of the Bekenstein-Hawking entropy,” Phys. Lett. B 379 (1996) 99–104, arXiv:hep-th/9601029.
  10. I. Bena, E. J. Martinec, S. D. Mathur, and N. P. Warner, “Fuzzballs and microstate geometries: Black-hole structure in string theory,” 2022. https://arxiv.org/abs/2204.13113.
  11. L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D 34 (1986) 373–383.
  12. M. Srednicki, “Entropy and area,” Phys. Rev. Lett. 71 (1993) 666–669, arXiv:hep-th/9303048.
  13. G. ’t Hooft, “On the Quantum Structure of a Black Hole,” Nucl. Phys. B 256 (1985) 727–745.
  14. T. Jacobson and A. Satz, “Black hole entanglement entropy and the renormalization group,” Phys. Rev. D 87 no. 8, (2013) 084047, arXiv:1212.6824 [hep-th].
  15. J. H. Cooperman and M. A. Luty, “Renormalization of Entanglement Entropy and the Gravitational Effective Action,” JHEP 12 (2014) 045, arXiv:1302.1878 [hep-th].
  16. V. Chandrasekaran, G. Penington, and E. Witten, “Large N algebras and generalized entropy,” arXiv:2209.10454 [hep-th].
  17. L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64 (2016) 24–43, arXiv:1403.5695 [hep-th]. [Addendum: Fortsch.Phys. 64, 44–48 (2016)].
  18. D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90 no. 12, (2014) 126007, arXiv:1406.2678 [hep-th].
  19. S. Aaronson, “The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes,” 7, 2016. arXiv:1607.05256 [quant-ph].
  20. V. Balasubramanian, M. Decross, A. Kar, and O. Parrikar, “Quantum Complexity of Time Evolution with Chaotic Hamiltonians,” JHEP 01 (2020) 134, arXiv:1905.05765 [hep-th].
  21. L. V. Iliesiu, M. Mezei, and G. Sárosi, “The volume of the black hole interior at late times,” JHEP 07 (2022) 073, arXiv:2107.06286 [hep-th].
  22. M. Sasieta, “Wormholes from heavy operator statistics in AdS/CFT,” JHEP 03 (2023) 158, arXiv:2211.11794 [hep-th].
  23. D. Marolf and H. Maxfield, “Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information,” JHEP 08 (2020) 044, arXiv:2002.08950 [hep-th].
  24. V. Balasubramanian, A. Kar, S. F. Ross, and T. Ugajin, “Spin structures and baby universes,” JHEP 09 (2020) 192, arXiv:2007.04333 [hep-th].
  25. V. Balasubramanian, A. Kar, Yue, C. Li, and O. Parrikar, “Quantum Error Correction in the Black Hole Interior,” arXiv:2203.01961 [hep-th].
  26. C. Akers, N. Engelhardt, D. Harlow, G. Penington, and S. Vardhan, “The black hole interior from non-isometric codes and complexity,” arXiv:2207.06536 [hep-th].
  27. A. Kar, “Non-Isometric Quantum Error Correction in Gravity,” arXiv:2210.13476 [hep-th].
  28. J. Chakravarty, “Overcounting of interior excitations: A resolution to the bags of gold paradox in AdS,” JHEP 02 (2021) 027, arXiv:2010.03575 [hep-th].
  29. R. Chao, B. W. Reichardt, C. Sutherland, and T. Vidick, “Overlapping qubits,” arXiv preprint arXiv:1701.01062 (2017) .
  30. J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, “Black Holes and Random Matrices,” JHEP 05 (2017) 118, arXiv:1611.04650 [hep-th]. [Erratum: JHEP 09, 002 (2018)].
  31. P. Saad, S. H. Shenker, and D. Stanford, “A semiclassical ramp in SYK and in gravity,” arXiv:1806.06840 [hep-th].
  32. P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th].
  33. T. G. Mertens and G. J. Turiaci, “Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity,” arXiv:2210.10846 [hep-th].
  34. J. Wheeler, “Relativity, groups and topology,” edited by B. S. DeWitt and C. M. DeWitt. Gordon and Breach, New York, 1964 .
  35. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “The entropy of Hawking radiation,” Rev. Mod. Phys. 93 no. 3, (2021) 035002, arXiv:2006.06872 [hep-th].
  36. A. R. Brown, H. Gharibyan, G. Penington, and L. Susskind, “The Python’s Lunch: geometric obstructions to decoding Hawking radiation,” JHEP 08 (2020) 121, arXiv:1912.00228 [hep-th].
  37. V. Balasubramanian, P. Caputa, J. M. Magan, and Q. Wu, “Quantum chaos and the complexity of spread of states,” Phys. Rev. D 106 no. 4, (2022) 046007, arXiv:2202.06957 [hep-th].
  38. V. Balasubramanian, J. M. Magan, and Q. Wu, “A Tale of Two Hungarians: Tridiagonalizing Random Matrices,” arXiv:2208.08452 [hep-th].
  39. I. Kim, E. Tang, and J. Preskill, “The ghost in the radiation: Robust encodings of the black hole interior,” JHEP 06 (2020) 031, arXiv:2003.05451 [hep-th].
  40. L. Susskind, L. Thorlacius, and J. Uglum, “The Stretched horizon and black hole complementarity,” Phys. Rev. D 48 (1993) 3743–3761, arXiv:hep-th/9306069.
  41. 1998.
  42. S. D. H. Hsu and D. Reeb, “Unitarity and the Hilbert space of quantum gravity,” Class. Quant. Grav. 25 (2008) 235007, arXiv:0803.4212 [hep-th].
  43. Z. Fu and D. Marolf, “Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT,” JHEP 11 (2019) 040, arXiv:1909.02505 [hep-th].
  44. I. Kourkoulou and J. Maldacena, “Pure states in the SYK model and nearly-A⁢d⁢S2𝐴𝑑subscript𝑆2AdS_{2}italic_A italic_d italic_S start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT gravity,” arXiv:1707.02325 [hep-th].
  45. A. Goel, H. T. Lam, G. J. Turiaci, and H. Verlinde, “Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK,” JHEP 02 (2019) 156, arXiv:1807.03916 [hep-th].
  46. J. Chandra and T. Hartman, “Coarse graining pure states in AdS/CFT,” arXiv:2206.03414 [hep-th].
  47. V. Balasubramanian, P. Kraus, A. E. Lawrence, and S. P. Trivedi, “Holographic probes of anti-de Sitter space-times,” Phys. Rev. D 59 (1999) 104021, arXiv:hep-th/9808017.
  48. T. Banks, M. R. Douglas, G. T. Horowitz, and E. J. Martinec, “AdS dynamics from conformal field theory,” arXiv:hep-th/9808016.
  49. V. Balasubramanian, S. B. Giddings, and A. E. Lawrence, “What do CFTs tell us about Anti-de Sitter space-times?,” JHEP 03 (1999) 001, arXiv:hep-th/9902052.
  50. A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74 (2006) 066009, arXiv:hep-th/0606141.
  51. V. Balasubramanian and P. Kraus, “A Stress tensor for Anti-de Sitter gravity,” Commun. Math. Phys. 208 (1999) 413–428, arXiv:hep-th/9902121.
  52. M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 07 (1998) 023, arXiv:hep-th/9806087.
  53. K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19 (2002) 5849–5876, arXiv:hep-th/0209067.
  54. W. Israel, “Singular hypersurfaces and thin shells in general relativity,” Nuovo Cim. B 44S10 (1966) 1. [Erratum: Nuovo Cim.B 48, 463 (1967)].
  55. J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 04 (2003) 021, arXiv:hep-th/0106112.
  56. R. Emparan, C. V. Johnson, and R. C. Myers, “Surface terms as counterterms in the AdS / CFT correspondence,” Phys. Rev. D 60 (1999) 104001, arXiv:hep-th/9903238.
  57. G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, “Replica wormholes and the black hole interior,” JHEP 03 (2022) 205, arXiv:1911.11977 [hep-th].
  58. D. Stanford, “More quantum noise from wormholes,” arXiv:2008.08570 [hep-th].
  59. J. Pollack, M. Rozali, J. Sully, and D. Wakeham, “Eigenstate thermalization and disorder averaging in gravity,” Phys. Rev. Lett. 125 (Jul, 2020) 021601. https://link.aps.org/doi/10.1103/PhysRevLett.125.021601.
  60. A. Maloney and E. Witten, “Averaging over Narain moduli space,” JHEP 10 (2020) 187, arXiv:2006.04855 [hep-th].
  61. J. Cotler and K. Jensen, “AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT gravity and random CFT,” JHEP 04 (2021) 033, arXiv:2006.08648 [hep-th].
  62. A. Altland and J. Sonner, “Late time physics of holographic quantum chaos,” SciPost Phys. 11 (2021) 034, arXiv:2008.02271 [hep-th].
  63. A. Altland, D. Bagrets, P. Nayak, J. Sonner, and M. Vielma, “From operator statistics to wormholes,” Phys. Rev. Res. 3 no. 3, (2021) 033259, arXiv:2105.12129 [hep-th].
  64. J. Chandra, S. Collier, T. Hartman, and A. Maloney, “Semiclassical 3D gravity as an average of large-c CFTs,” arXiv:2203.06511 [hep-th].
  65. P. Betzios, E. Kiritsis, and O. Papadoulaki, “Interacting systems and wormholes,” JHEP 02 (2022) 126, arXiv:2110.14655 [hep-th].
  66. J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys. Rev. A 43 (Feb, 1991) 2046–2049. https://link.aps.org/doi/10.1103/PhysRevA.43.2046.
  67. M. Srednicki, “Chaos and quantum thermalization,” Physical Review E 50 no. 2, (Aug, 1994) 888–901.
  68. A. Belin and J. de Boer, “Random statistics of OPE coefficients and Euclidean wormholes,” Class. Quant. Grav. 38 no. 16, (2021) 164001, arXiv:2006.05499 [hep-th].
  69. D. L. Jafferis, D. K. Kolchmeyer, B. Mukhametzhanov, and J. Sonner, “Matrix models for eigenstate thermalization,” arXiv:2209.02130 [hep-th].
  70. J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,” JHEP 08 (2016) 106, arXiv:1503.01409 [hep-th].
  71. V. Balasubramanian, V. Jejjala, and J. Simon, “The Library of Babel,” Int. J. Mod. Phys. D 14 (2005) 2181–2186, arXiv:hep-th/0505123.
  72. V. Balasubramanian, J. de Boer, V. Jejjala, and J. Simon, “The Library of Babel: On the origin of gravitational thermodynamics,” JHEP 12 (2005) 006, arXiv:hep-th/0508023.
  73. P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th].
  74. J. Pollack, M. Rozali, J. Sully, and D. Wakeham, “Eigenstate Thermalization and Disorder Averaging in Gravity,” Phys. Rev. Lett. 125 no. 2, (2020) 021601, arXiv:2002.02971 [hep-th].
  75. J.-M. Schlenker and E. Witten, “No ensemble averaging below the black hole threshold,” JHEP 07 (2022) 143, arXiv:2202.01372 [hep-th].
  76. T. Guhr, A. Muller-Groeling, and H. A. Weidenmuller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept. 299 (1998) 189–425, arXiv:cond-mat/9707301.
  77. K. Papadodimas and S. Raju, “Local Operators in the Eternal Black Hole,” Phys. Rev. Lett. 115 no. 21, (2015) 211601, arXiv:1502.06692 [hep-th].
  78. H. Verlinde, “Deconstructing the Wormhole: Factorization, Entanglement and Decoherence,” arXiv:2105.02142 [hep-th].
  79. A. del Campo, J. Molina-Vilaplana, and J. Sonner, “Scrambling the spectral form factor: unitarity constraints and exact results,” Phys. Rev. D 95 no. 12, (2017) 126008, arXiv:1702.04350 [hep-th].
  80. D. Stanford and Z. Yang, “Firewalls from wormholes,” arXiv:2208.01625 [hep-th].
  81. P. Saad, D. Stanford, Z. Yang, and S. Yao, “A convergent genus expansion for the plateau,” arXiv:2210.11565 [hep-th].
  82. A. Blommaert, J. Kruthoff, and S. Yao, “An integrable road to a perturbative plateau,” arXiv:2208.13795 [hep-th].
  83. G. ’t Hooft, “Dimensional reduction in quantum gravity,” Conf. Proc. C 930308 (1993) 284–296, arXiv:gr-qc/9310026.
  84. L. Susskind, “The World as a hologram,” J. Math. Phys. 36 (1995) 6377–6396, arXiv:hep-th/9409089.
  85. R. Bousso, “A Covariant entropy conjecture,” JHEP 07 (1999) 004, arXiv:hep-th/9905177.
  86. P.-S. Hsin, L. V. Iliesiu, and Z. Yang, “A violation of global symmetries from replica wormholes and the fate of black hole remnants,” Class. Quant. Grav. 38 no. 19, (2021) 194004, arXiv:2011.09444 [hep-th].
  87. P. Cvitanović, “Planar perturbation expansion,” Physics Letters B 99 no. 1, (1981) 49–52. https://www.sciencedirect.com/science/article/pii/0370269381908017.
  88. R. Speicher, “Free probability theory,” 2009. https://arxiv.org/abs/0911.0087.
  89. Oxford University Press, 09, 2015.
  90. D. Stanford and E. Witten, “Fermionic Localization of the Schwarzian Theory,” JHEP 10 (2017) 008, arXiv:1703.04612 [hep-th].
  91. L. V. Iliesiu and G. J. Turiaci, “The statistical mechanics of near-extremal black holes,” JHEP 05 (2021) 145, arXiv:2003.02860 [hep-th].
  92. J. Boruch, L. V. Iliesiu, and C. Yan, “Constructing all BPS black hole microstates from the gravitational path integral,” arXiv:2307.13051 [hep-th].
  93. A. Climent, R. Emparan, J. Magan, M. Sasieta, A. V. Lopez, “To appear,”.
  94. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation,” JHEP 05 (2020) 013, arXiv:1911.12333 [hep-th].
  95. G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox,” JHEP 09 (2020) 002, arXiv:1905.08255 [hep-th].
  96. 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 12 (2019) 063, arXiv:1905.08762 [hep-th].
  97. A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, “The Page curve of Hawking radiation from semiclassical geometry,” JHEP 03 (2020) 149, arXiv:1908.10996 [hep-th].
  98. D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett. 71 (1993) 1291–1294, arXiv:gr-qc/9305007.
  99. D. N. Page, “Information in black hole radiation,” Phys. Rev. Lett. 71 (1993) 3743–3746, arXiv:hep-th/9306083.
  100. G. Sárosi, “AdS22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT holography and the SYK model,” PoS Modave2017 (2018) 001, arXiv:1711.08482 [hep-th].
  101. V. Balasubramanian, A. Kar, O. Parrikar, G. Sárosi, and T. Ugajin, “Geometric secret sharing in a model of Hawking radiation,” JHEP 01 (2021) 177, arXiv:2003.05448 [hep-th].
  102. H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, and S. Shashi, “Inconsistency of islands in theories with long-range gravity,” JHEP 01 (2022) 182, arXiv:2107.03390 [hep-th].
  103. V. Balasubramanian, A. Kar, and T. Ugajin, “Entanglement between two gravitating universes,” Class. Quant. Grav. 39 no. 17, (2022) 174001, arXiv:2104.13383 [hep-th].
  104. L. Susskind, “Black Holes at Exp-time,” arXiv:2006.01280 [hep-th].
  105. J. M. Magán, “Black holes, complexity and quantum chaos,” JHEP 09 (2018) 043, arXiv:1805.05839 [hep-th].
  106. J. M. Magán and J. Simón, “On operator growth and emergent Poincaré symmetries,” JHEP 05 (2020) 071, arXiv:2002.03865 [hep-th].
  107. P. Caputa, J. M. Magan, and D. Patramanis, “Geometry of Krylov complexity,” Phys. Rev. Res. 4 no. 1, (2022) 013041, arXiv:2109.03824 [hep-th].
  108. L. V. Iliesiu, S. Murthy, and G. J. Turiaci, “Black hole microstate counting from the gravitational path integral,” arXiv:2209.13602 [hep-th].
  109. V. Balasubramanian, A. Lawrence, J. M. Magan, and M. Sasieta, “Microscopic origin of the entropy of astrophysical black holes,” arXiv:2212.08623 [hep-th].
  110. A. N. Kolmogorov, “Three approaches to the quantitative definition of information,” International Journal of Computer Mathematics 2 no. 1-4, (1968) 157–168.
  111. C. Lanczos, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” Journal of research of the National Bureau of Standards 45 (1950) 255–282.
  112. V. S. Viswanath and G. Müller, “The recursion method : application to many-body dynamics,” 1994.
  113. D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, “A Universal Operator Growth Hypothesis,” Phys. Rev. X 9 no. 4, (2019) 041017, arXiv:1812.08657 [cond-mat.stat-mech].
Citations (49)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up