Abstract
We describe the experience of an observer falling into a black hole using the AdS/CFT correspondence. In order to do this, we reconstruct the local bulk operators measured by the observer along his trajectory outside the black hole. We then extend our construction beyond the black hole horizon. We show that this is possible because of an effective doubling of the observables in the boundary theory, when it is in a purestate that is close to the thermal state. Our construction allows us to rephrase questions about information-loss and the structure of the metric at the horizon in terms of more familiar CFT correlators. It suggests that to precisely identify black-hole microstates, the observer would need to conduct measurements to an accuracy of \( {e^{{-{S_{\mathrm{BH}}}}}} \). This appears to be inconsistent with the “fuzzball” proposal, and other recent proposals in which pure states in the ensemble of the black hole are represented by macroscopically distinct geometries. Furthermore, our description of the black hole interior in terms of CFT operators provides a natural realization of black hole complementarity and a method of preserving unitarity without “firewalls.”
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References
S.D. Mathur, The information paradox: conflicts and resolutions, Pramana 79 (2012) 1059 [arXiv:1201.2079] [INSPIRE].
S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [INSPIRE].
O. Lunin, S.D. Mathur and A. Saxena, What is the gravity dual of a chiral primary?, Nucl. Phys. B 655 (2003) 185 [hep-th/0211292] [INSPIRE].
O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
R. Bousso, Complementarity is not enough, Phys. Rev. D 87 (2013) 124023 [arXiv:1207.5192] [INSPIRE].
Y. Nomura, J. Varela and S.J. Weinberg, Complementarity endures: no firewall for an infalling observer, JHEP 03 (2013) 059 [arXiv:1207.6626] [INSPIRE].
S.D. Mathur and D. Turton, Comments on black holes I: the possibility of complementarity, arXiv:1208.2005 [INSPIRE].
L. Susskind, Singularities, firewalls and complementarity, arXiv:1208.3445 [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Non-extremal black hole microstates: fuzzballs of fire or fuzzballs of fuzz?, JHEP 12 (2012) 014 [arXiv:1208.3468] [INSPIRE].
A. Giveon and N. Itzhaki, String theory versus black hole complementarity, JHEP 12 (2012) 094 [arXiv:1208.3930] [INSPIRE].
T. Banks and W. Fischler, Holographic space-time does not predict firewalls, arXiv:1208.4757 [INSPIRE].
A. Ori, Firewall or smooth horizon?, arXiv:1208.6480 [INSPIRE].
R. Brustein, Origin of the blackhole information paradox, arXiv:1209.2686 [INSPIRE].
L. Susskind, The transfer of entanglement: the case for firewalls, arXiv:1210.2098 [INSPIRE].
D. Marolf and A.C. Wall, Eternal black holes and superselection in AdS/CFT, Class. Quant. Grav. 30 (2013) 025001 [arXiv:1210.3590] [INSPIRE].
S. Hossenfelder, Comment on the black hole firewall, arXiv:1210.5317 [INSPIRE].
Y. Nomura, J. Varela and S.J. Weinberg, Black holes, information and Hilbert space for quantum gravity, Phys. Rev. D 87 (2013) 084050 [arXiv:1210.6348] [INSPIRE].
D.-I. Hwang, B.-H. Lee and D.-H. Yeom, Is the firewall consistent?: gedanken experiments on black hole complementarity and firewall proposal, JCAP 01 (2013) 005 [arXiv:1210.6733] [INSPIRE].
K. Larjo, D.A. Lowe and L. Thorlacius, Black holes without firewalls, Phys. Rev. D 87 (2013) 104018 [arXiv:1211.4620] [INSPIRE].
S.L. Braunstein, S. Pirandola and K. Życzkowski, Entangled black holes as ciphers of hidden information, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
S.G. Avery, B.D. Chowdhury and A. Puhm, Unitarity and fuzzball complementarity: ‘Alice fuzzes but may not even know it!’, JHEP 09 (2013) 012 [arXiv:1210.6996] [INSPIRE].
B.D. Chowdhury and A. Puhm, Is Alice burning or fuzzing?, Phys. Rev. D 88 (2013) 063509 [arXiv:1208.2026] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about anti-de Sitter space-times?, JHEP 03 (1999) 001 [hep-th/9902052] [INSPIRE].
I. Bena, On the construction of local fields in the bulk of AdS 5 and other spaces, Phys. Rev. D 62 (2000) 066007 [hep-th/9905186] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: a holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. D 75 (2007) 129902] [hep-th/0612053] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: a boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT and the fate of the BTZ singularity, arXiv:0710.4334 [INSPIRE].
M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [Int. J. Mod. Phys. D 19 (2010) 2429] [arXiv:1005.3035] [INSPIRE].
M. Van Raamsdonk, A patchwork description of dual spacetimes in AdS/CFT, Class. Quant. Grav. 28 (2011) 065002 [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The gravity dual of a density matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and transhorizon measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent spacetime and holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
Y. Kiem, H.L. Verlinde and E.P. Verlinde, Black hole horizons and complementarity, Phys. Rev. D 52 (1995) 7053 [hep-th/9502074] [INSPIRE].
V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
S.B. Giddings and M. Lippert, Precursors, black holes and a locality bound, Phys. Rev. D 65 (2002) 024006 [hep-th/0103231] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
V.E. Hubeny, Precursors see inside black holes, Int. J. Mod. Phys. D 12 (2003) 1693 [hep-th/0208047] [INSPIRE].
P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [INSPIRE].
T.S. Levi and S.F. Ross, Holography beyond the horizon and cosmic censorship, Phys. Rev. D 68 (2003) 044005 [hep-th/0304150] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
J. Barbon and E. Rabinovici, Very long time scales and black hole thermal equilibrium, JHEP 11 (2003) 047 [hep-th/0308063] [INSPIRE].
J. Kaplan, Extracting data from behind horizons with the AdS/CFT correspondence, hep-th/0402066 [INSPIRE].
V. Balasubramanian and T.S. Levi, Beyond the veil: inner horizon instability and holography, Phys. Rev. D 70 (2004) 106005 [hep-th/0405048] [INSPIRE].
G. Festuccia and H. Liu, Excursions beyond the horizon: black hole singularities in Yang-Mills theories. I, JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The library of Babel: on the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [INSPIRE].
V. Balasubramanian, P. Kraus and M. Shigemori, Massless black holes and black rings as effective geometries of the D1-D5 system, Class. Quant. Grav. 22 (2005) 4803 [hep-th/0508110] [INSPIRE].
G. Festuccia and H. Liu, The arrow of time, black holes and quantum mixing of large-N Yang-Mills theories, JHEP 12 (2007) 027 [hep-th/0611098] [INSPIRE].
V. Balasubramanian et al., Typicality versus thermality: an analytic distinction, Gen. Rel. Grav. 40 (2008) 1863 [hep-th/0701122] [INSPIRE].
D. Marolf, Unitarity and holography in gravitational physics, Phys. Rev. D 79 (2009) 044010 [arXiv:0808.2842] [INSPIRE].
V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black holes as effective geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [INSPIRE].
J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, A bound on the entropy of supergravity?, JHEP 02 (2010) 062 [arXiv:0906.0011] [INSPIRE].
G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [INSPIRE].
V. Balasubramanian and B. Czech, Quantitative approaches to information recovery from black holes, Class. Quant. Grav. 28 (2011) 163001 [arXiv:1102.3566] [INSPIRE].
S.G. Avery, Qubit models of black hole evaporation, JHEP 01 (2013) 176 [arXiv:1109.2911] [INSPIRE].
J. Simon, Extremal black holes, holography and coarse graining, Int. J. Mod. Phys. A 26 (2011) 1903 [arXiv:1106.0116] [INSPIRE].
R. Bousso, B. Freivogel, S. Leichenauer, V. Rosenhaus and C. Zukowski, Null geodesics, local CFT operators and AdS/CFT for subregions, Phys. Rev. D 88 (2013) 064057 [arXiv:1209.4641] [INSPIRE].
M. Lüscher and G. Mack, Global conformal invariance in quantum field theory, Commun. Math. Phys. 41 (1975) 203 [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].
W. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
N. Birrell and P. Davies, Quantum fields in curved space, Cambridge Univ. Press, Cambridge U.K. (1986).
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
Y. Takahashi and H. Umezawa, Thermo field dynamics, Int. J. Mod. Phys. B 10 (1996) 1755 [INSPIRE].
J. von Neumann, Proof of the ergodic theorem and the H-theorem in quantum mechanics, Eur. Phys. J. H 35 (2010) 201 [arXiv:1003.2133].
J. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.
M. Srednicki, The approach to thermal equilibrium in quantized chaotic systems, J. Phys. A 32 (1999) 1163 [cond-mat/9809360].
S.D. Mathur, What the information paradox is not, arXiv:1108.0302 [INSPIRE].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
D. Kabat, G. Lifschytz and D.A. Lowe, Constructing local bulk observables in interacting AdS/CFT, Phys. Rev. D 83 (2011) 106009 [arXiv:1102.2910] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
I. Heemskerk and J. Sully, More holography from conformal field theory, JHEP 09 (2010) 099 [arXiv:1006.0976] [INSPIRE].
A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective conformal theory and the flat-space limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, AdS field theory from conformal field theory, JHEP 02 (2013) 054 [arXiv:1208.0337] [INSPIRE].
D. Kabat, G. Lifschytz, S. Roy and D. Sarkar, Holographic representation of bulk fields with spin in AdS/CFT, Phys. Rev. D 86 (2012) 026004 [arXiv:1204.0126] [INSPIRE].
J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
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Papadodimas, K., Raju, S. An infalling observer in AdS/CFT. J. High Energ. Phys. 2013, 212 (2013). https://doi.org/10.1007/JHEP10(2013)212
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DOI: https://doi.org/10.1007/JHEP10(2013)212