Abstract
We study how the black hole complementarity principle can emerge from quantum gravitational dynamics within a local semiclassical approximation. Further developing and then simplifying a microstate model based on the fragmentation instability of a near-extremal black hole, we find that the key to the replication (but not cloning) of infalling information is the decoupling of various degrees of freedom. The infalling matter decouples from the interior retaining a residual time-dependent quantum state in the hair which encodes the initial state of the matter non-isometrically. The non-linear ringdown of the interior after energy absorption and decoupling also encodes the initial state, and transfers the information to Hawking radiation. During the Hawking evaporation process, the fragmented throats decouple from each other and the hair decouples from the throats. We find that the hair mirrors infalling information after the decoupling time which scales with the logarithm of the entropy (at the time of infall) when the average mass per fragmented throat (a proxy for the temperature) is held fixed. The decoding protocol for the mirrored information does not require knowledge of the interior, and only limited information from the Hawking radiation, as can be argued to be necessitated by the complementarity principle. We discuss the scope of the model to illuminate various aspects of information processing in a black hole.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].
D. Harlow, Jerusalem Lectures on Black Holes and Quantum Information, Rev. Mod. Phys. 88 (2016) 015002 [arXiv:1409.1231] [INSPIRE].
S. Raju, Lessons from the information paradox, Phys. Rept. 943 (2022) 1 [arXiv:2012.05770] [INSPIRE].
T. Kibe, P. Mandayam and A. Mukhopadhyay, Holographic spacetime, black holes and quantum error correcting codes: a review, Eur. Phys. J. C 82 (2022) 463 [arXiv:2110.14669] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S.L. Braunstein, S. Pirandola and K. Życzkowski, Better Late than Never: Information Retrieval from Black Holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
C. Akers et al., The black hole interior from non-isometric codes and complexity, arXiv:2207.06536 [INSPIRE].
K. Jacobs and D.A. Steck, A straightforward introduction to continuous quantum measurement, Contemp. Phys. 47 (2006) 279.
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] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
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] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri et al., Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
T. Kibe, A. Mukhopadhyay, A. Soloviev and H. Swain, SL(2, R) lattices as information processors, Phys. Rev. D 102 (2020) 086008 [arXiv:2006.08644] [INSPIRE].
D. Brill, Splitting of an extremal Reissner-Nordstrom throat via quantum tunneling, Phys. Rev. D 46 (1992) 1560 [hep-th/9202037] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
S.D. Mathur, The Fuzzball proposal for black holes: An Elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
I. Bena, E.J. Martinec, S.D. Mathur and N.P. Warner, Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory, arXiv:2204.13113 [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
J.D. Brown, Lower Dimensional Gravity, World Scientific (1988) [https://doi.org/10.1142/0622].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
L.K. Joshi, A. Mukhopadhyay and A. Soloviev, Time-dependent NAdS2 holography with applications, Phys. Rev. D 101 (2020) 066001 [arXiv:1901.08877] [INSPIRE].
S. Sachdev, Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and charged black holes, arXiv:2304.13744 [INSPIRE].
I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS2 gravity, arXiv:1707.02325 [INSPIRE].
A. Georges, G. Kotliar, W. Krauth and M.J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68 (1996) 13 [INSPIRE].
C. Ecker et al., Time evolution of a toy semiholographic glasma, JHEP 08 (2018) 074 [arXiv:1806.01850] [INSPIRE].
S. Mondkar, A. Mukhopadhyay, A. Rebhan and A. Soloviev, Quasinormal modes of a semi-holographic black brane and thermalization, JHEP 11 (2021) 080 [arXiv:2108.02788] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
H.R. Lewis, Classical and Quantum Systems with Time-Dependent Harmonic-Oscillator-Type Hamiltonians, Phys. Rev. Lett. 18 (1967) 510.
J.R. Choi, Coherent states of general time-dependent harmonic oscillator, Pramana 62 (2004) 13.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
D.N. Page, Time Dependence of Hawking Radiation Entropy, JCAP 09 (2013) 028 [arXiv:1301.4995] [INSPIRE].
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
S. Aaronson, The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes, arXiv:1607.05256 [INSPIRE].
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] [INSPIRE].
Z. Gyongyosi et al., Black Hole Information Recovery in JT Gravity, arXiv:2209.11774 [https://doi.org/10.1007/JHEP01(2023)139] [INSPIRE].
Z. Gyongyosi et al., The holographic map of an evaporating black hole, JHEP 07 (2023) 043 [arXiv:2301.08362] [INSPIRE].
P. Gao, D.L. Jafferis and A.C. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
T. Kibe, A. Mukhopadhyay and P. Roy, Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition, Phys. Rev. Lett. 128 (2022) 191602 [arXiv:2109.09914] [INSPIRE].
A. Banerjee et al., Erasure Tolerant Quantum Memory and the Quantum Null Energy Condition in Holographic Systems, Phys. Rev. Lett. 129 (2022) 191601 [arXiv:2202.00022] [INSPIRE].
S. Leutheusser and H. Liu, Emergent times in holographic duality, arXiv:2112.12156 [INSPIRE].
E. Witten, Gravity and the crossed product, JHEP 10 (2022) 008 [arXiv:2112.12828] [INSPIRE].
G. Penington and E. Witten, Algebras and States in JT Gravity, arXiv:2301.07257 [INSPIRE].
D.K. Kolchmeyer, von Neumann algebras in JT gravity, JHEP 06 (2023) 067 [arXiv:2303.04701] [INSPIRE].
S. Ali Ahmad and R. Jefferson, Crossed product algebras and generalized entropy for subregions, arXiv:2306.07323 [INSPIRE].
K. Jensen, J. Sorce and A. Speranza, Generalized entropy for general subregions in quantum gravity, arXiv:2306.01837 [INSPIRE].
N. Bao et al., Branches of the Black Hole Wave Function Need Not Contain Firewalls, Phys. Rev. D 97 (2018) 126014 [arXiv:1712.04955] [INSPIRE].
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016) 239 [arXiv:1509.06411] [INSPIRE].
D.L. Jafferis, D.K. Kolchmeyer, B. Mukhametzhanov and J. Sonner, Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices, Phys. Rev. D 108 (2023) 066015 [arXiv:2209.02131] [INSPIRE].
S. Sachdev, Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and strange metals, arXiv:2305.01001 [INSPIRE].
B. Douçot, A. Mukhopadhyay, G. Policastro and S. Samanta, Linear-in-T resistivity from semiholographic non-Fermi liquid models, Phys. Rev. D 104 (2021) L081901 [arXiv:2012.15679] [INSPIRE].
H. Swain et al., A simple model for strange metallic behavior, arXiv:2206.01215 [INSPIRE].
S. Das, S.K. Garg, C. Krishnan and A. Kundu, Fuzzballs and random matrices, JHEP 10 (2023) 031 [arXiv:2301.11780] [INSPIRE].
V. Balasubramanian, A. Lawrence, J.M. Magan and M. Sasieta, Microscopic origin of the entropy of black holes in general relativity, arXiv:2212.02447 [INSPIRE].
V. Balasubramanian, A. Lawrence, J.M. Magan and M. Sasieta, Microscopic origin of the entropy of astrophysical black holes, arXiv:2212.08623 [INSPIRE].
Acknowledgments
It is a pleasure to thank Rajesh Gopakumar, Alok Laddha, Prabha Mandayam, Giuseppe Policastro, Suvrat Raju, Ashoke Sen and Sai Vinjanampathy for many helpful discussions. The research of TK is supported by the Prime Minister’s Research Fellowship (PMRF). AM acknowledges the support of the Ramanujan Fellowship of the Science and Engineering Board of the Department of Science and Technology of India, the new faculty seed grant of IIT Madras and the additional support from the Institute of Eminence scheme of IIT Madras funded by the Ministry of Education of India. HS acknowledges support from the INSPIRE PhD Fellowship of Department of Science and Technology of India.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2307.04799
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kibe, T., Mondkar, S., Mukhopadhyay, A. et al. Black hole complementarity from microstate models: a study of information replication and the encoding in the black hole interior. J. High Energ. Phys. 2023, 96 (2023). https://doi.org/10.1007/JHEP10(2023)096
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2023)096