Abstract
We consider the issue of information recovery for an object carrying energy and entropy into a black hole using the generalized entropy formalism, in the context of JT gravity where the backreaction problem can be solved exactly. We verify the main aspects of the Hayden-Preskill scenario but with some refinements. We show that the information is encoded in the Hawking radiation in a redundant way, as expected for a quantum error correcting code. We show how quantum extremal surfaces associated to information recovery have the form of a python’s lunch and thereby show that the complexity of decoding is exponential in a combination of the entropy shift of the black hole and the entropy of the object. We also show that an infalling observer must have a smooth experience at the horizon and we calculate their endurance proper time inside the black hole before they are radiated out.
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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].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [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].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
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].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [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, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
K. Goto, T. Hartman and A. Tajdini, Replica wormholes for an evaporating 2D black hole, JHEP 04 (2021) 289 [arXiv:2011.09043] [INSPIRE].
D. Marolf and H. Maxfield, Observations of Hawking radiation: the Page curve and baby universes, JHEP 04 (2021) 272 [arXiv:2010.06602] [INSPIRE].
S. Colin-Ellerin, X. Dong, D. Marolf, M. Rangamani and Z. Wang, Real-time gravitational replicas: Formalism and a variational principle, JHEP 05 (2021) 117 [arXiv:2012.00828] [INSPIRE].
T.J. Hollowood and S.P. Kumar, Islands and Page Curves for Evaporating Black Holes in JT Gravity, JHEP 08 (2020) 094 [arXiv:2004.14944] [INSPIRE].
T.J. Hollowood, S. Prem Kumar and A. Legramandi, Hawking radiation correlations of evaporating black holes in JT gravity, J. Phys. A 53 (2020) 475401 [arXiv:2007.04877] [INSPIRE].
T.J. Hollowood, S.P. Kumar, A. Legramandi and N. Talwar, Islands in the stream of Hawking radiation, JHEP 11 (2021) 067 [arXiv:2104.00052] [INSPIRE].
T.J. Hollowood, S.P. Kumar, A. Legramandi and N. Talwar, Ephemeral islands, plunging quantum extremal surfaces and BCFT channels, JHEP 01 (2022) 078 [arXiv:2109.01895] [INSPIRE].
T.J. Hollowood, S.P. Kumar, A. Legramandi and N. Talwar, Grey-body factors, irreversibility and multiple island saddles, JHEP 03 (2022) 110 [arXiv:2111.02248] [INSPIRE].
R. Bousso and A. Shahbazi-Moghaddam, Island Finder and Entropy Bound, Phys. Rev. D 103 (2021) 106005 [arXiv:2101.11648] [INSPIRE].
X. Wang, R. Li and J. Wang, Islands and Page curves of Reissner-Nordström black holes, JHEP 04 (2021) 103 [arXiv:2101.06867] [INSPIRE].
G.K. Karananas, A. Kehagias and J. Taskas, Islands in linear dilaton black holes, JHEP 03 (2021) 253 [arXiv:2101.00024] [INSPIRE].
J. Kumar Basak, D. Basu, V. Malvimat, H. Parihar and G. Sengupta, Islands for entanglement negativity, SciPost Phys. 12 (2022) 003 [arXiv:2012.03983] [INSPIRE].
Y. Matsuo, Islands and stretched horizon, JHEP 07 (2021) 051 [arXiv:2011.08814] [INSPIRE].
J. Hernandez, R.C. Myers and S.-M. Ruan, Quantum extremal islands made easy. Part III. Complexity on the brane, JHEP 02 (2021) 173 [arXiv:2010.16398] [INSPIRE].
Y. Ling, Y. Liu and Z.-Y. Xian, Island in Charged Black Holes, JHEP 03 (2021) 251 [arXiv:2010.00037] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, JHEP 12 (2020) 025 [arXiv:2010.00018] [INSPIRE].
H.Z. Chen, Z. Fisher, J. Hernandez, R.C. Myers and S.-M. Ruan, Evaporating Black Holes Coupled to a Thermal Bath, JHEP 01 (2021) 065 [arXiv:2007.11658] [INSPIRE].
V. Chandrasekaran, M. Miyaji and P. Rath, Including contributions from entanglement islands to the reflected entropy, Phys. Rev. D 102 (2020) 086009 [arXiv:2006.10754] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane, JHEP 10 (2020) 166 [arXiv:2006.04851] [INSPIRE].
K. Hashimoto, N. Iizuka and Y. Matsuo, Islands in Schwarzschild black holes, JHEP 06 (2020) 085 [arXiv:2004.05863] [INSPIRE].
F.F. Gautason, L. Schneiderbauer, W. Sybesma and L. Thorlacius, Page Curve for an Evaporating Black Hole, JHEP 05 (2020) 091 [arXiv:2004.00598] [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].
K. Kawabata, T. Nishioka, Y. Okuyama and K. Watanabe, Probing Hawking radiation through capacity of entanglement, JHEP 05 (2021) 062 [arXiv:2102.02425] [INSPIRE].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE].
A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model, JHEP 05 (2021) 135 [arXiv:2103.15852] [INSPIRE].
G. Grimaldi, J. Hernandez and R.C. Myers, Quantum extremal islands made easy. Part IV. Massive black holes on the brane, JHEP 03 (2022) 136 [arXiv:2202.00679] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
K. Ghosh and C. Krishnan, Dirichlet baths and the not-so-fine-grained Page curve, JHEP 08 (2021) 119 [arXiv:2103.17253] [INSPIRE].
C. Akers, N. Engelhardt, D. Harlow, G. Penington and S. Vardhan, The black hole interior from non-isometric codes and complexity, arXiv:2207.06536 [INSPIRE].
C. Akers and G. Penington, Quantum minimal surfaces from quantum error correction, SciPost Phys. 12 (2022) 157 [arXiv:2109.14618] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [INSPIRE].
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] [INSPIRE].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
N. Engelhardt, G. Penington and A. Shahbazi-Moghaddam, Finding pythons in unexpected places, Class. Quant. Grav. 39 (2022) 094002 [arXiv:2105.09316] [INSPIRE].
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
H. Casini, Relative entropy and the Bekenstein bound, Class. Quant. Grav. 25 (2008) 205021 [arXiv:0804.2182] [INSPIRE].
J.D. Bekenstein, A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems, Phys. Rev. D 23 (1981) 287 [INSPIRE].
D. Harlow, TASI Lectures on the Emergence of Bulk Physics in AdS/CFT, PoS TASI2017 (2018) 002 [arXiv:1802.01040] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [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].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
B. Yoshida and A. Kitaev, Efficient decoding for the Hayden-Preskill protocol, arXiv:1710.03363 [INSPIRE].
B. Yoshida, Firewalls vs. Scrambling, JHEP 10 (2019) 132 [arXiv:1902.09763] [INSPIRE].
R. Bousso and A. Shahbazi-Moghaddam, Quantum Singularities, arXiv:2206.07001 [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
B. Yoshida, Soft mode and interior operator in the Hayden-Preskill thought experiment, Phys. Rev. D 100 (2019) 086001 [arXiv:1812.07353] [INSPIRE].
B. Yoshida, Observer-dependent black hole interior from operator collision, Phys. Rev. D 103 (2021) 046004 [arXiv:1910.11346] [INSPIRE].
B. Yoshida, Recovery algorithms for Clifford Hayden-Preskill problem, arXiv:2106.15628 [INSPIRE].
H. Casini, C.D. Fosco and M. Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions, J. Stat. Mech. 0507 (2005) P07007 [cond-mat/0505563] [INSPIRE].
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Gyongyosi, Z., Hollowood, T.J., Kumar, S.P. et al. Black hole information recovery in JT gravity. J. High Energ. Phys. 2023, 139 (2023). https://doi.org/10.1007/JHEP01(2023)139
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DOI: https://doi.org/10.1007/JHEP01(2023)139