Abstract
The unitary evaporation of a black hole (BH) in an initially pure state must lead to the eventual purification of the emitted radiation. It follows that the late radiation has to be entangled with the early radiation and, as a consequence, the entanglement among the Hawking pair partners has to decrease continuously from maximal to vanishing during the BH’s life span. Starting from the basic premise that both the horizon radius and the center of mass of a finite-mass BH are fluctuating quantum mechanically, we show how this process is realized. First, it is shown that the horizon fluctuations induce a small amount of variance in the total linear momentum of each created pair. This is in contrast to the case of an infinitely massive BH, for which the total momentum of the produced pair vanishes exactly on account of momentum conservation. This variance leads to a random recoil of the BH during each emission and, as a result, the center of mass of the BH undergoes a quantum random walk. Consequently, the uncertainty in its momentum grows as the square root of the number of emissions. We then show that this uncertainty controls the amount of deviation from maximal entanglement of the produced pairs and that this deviation is determined by the ratio of the cumulative number of emitted particles to the initial BH entropy. Thus, the interplay between the horizon and center-of-mass fluctuations provides a mechanism for teleporting entanglement from the pair partners to the BH and the emitted radiation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
D.N. Page, Black hole information, hep-th/9305040 [INSPIRE].
S.D. Mathur, What Exactly is the Information Paradox?, Lect. Notes Phys. 769 (2009) 3 [arXiv:0803.2030] [INSPIRE].
S.D. Mathur, The information paradox: A pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
S.D. Mathur, What the information paradox is not, arXiv:1108.0302 [INSPIRE].
S.D. Mathur, What does strong subadditivity tell us about black holes?, Nucl. Phys. Proc. Suppl. 251-252 (2014) 16 [arXiv:1309.6583] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Pair creation in non-extremal fuzzball geometries, Class. Quant. Grav. 25 (2008) 225021 [arXiv:0806.2309] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Non-extremal fuzzballs and ergoregion emission, Class. Quant. Grav. 26 (2009) 035006 [arXiv:0810.2951] [INSPIRE].
S.D. Mathur, Fuzzballs, Firewalls and all that…, to be published.
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
N. Itzhaki, Is the black hole complementarity principle really necessary?, hep-th/9607028 [INSPIRE].
G. ’t Hooft, The selfscreening Hawking atmosphere: A new approach to quantum black hole microstates, Nucl. Phys. Proc. Suppl. 68 (1998) 174 [gr-qc/9706058] [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].
D. Marolf and J. Polchinski, Gauge/Gravity Duality and the Black Hole Interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].
R. Bousso, Firewalls from double purity, Phys. Rev. D 88 (2013) 084035 [arXiv:1308.2665] [INSPIRE].
R. Bousso, Violations of the Equivalence Principle by a Nonlocally Reconstructed Vacuum at the Black Hole Horizon, Phys. Rev. Lett. 112 (2014) 041102 [arXiv:1308.3697] [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
R. Brustein and A.J.M. Medved, Black hole firewalls, smoke and mirrors, Phys. Rev. D 90 (2014) 024040 [arXiv:1401.1401] [INSPIRE].
R. Brustein and A.J.M. Medved, Falling through the black hole horizon, JHEP 06 (2015) 089 [arXiv:1503.05597] [INSPIRE].
R. Brustein, Origin of the blackhole information paradox, Fortsch. Phys. 62 (2014) 255 [arXiv:1209.2686] [INSPIRE].
G. Dvali and C. Gomez, Black Hole’s Quantum N-Portrait, Fortsch. Phys. 61 (2013) 742 [arXiv:1112.3359] [INSPIRE].
M. Visser, Physical observability of horizons, Phys. Rev. D 90 (2014) 127502 [arXiv:1407.7295] [INSPIRE].
R. Brustein and A.J.M. Medved, Restoring predictability in semiclassical gravitational collapse, JHEP 09 (2013) 015 [arXiv:1305.3139] [INSPIRE].
R. Brustein and A.J.M. Medved, Phases of information release during black hole evaporation, JHEP 02 (2014) 116 [arXiv:1310.5861] [INSPIRE].
R. Brustein and A.J.M. Medved, Horizons of semiclassical black holes are cold, JHEP 06 (2014) 057 [arXiv:1312.0880] [INSPIRE].
G. Dvali and C. Gomez, Black Hole’s Quantum N-Portrait, Fortsch. Phys. 61 (2013) 742 [arXiv:1112.3359] [INSPIRE].
R. Brustein and A.J.M. Medved, Quantum state of the black hole interior, JHEP 08 (2015) 082 [arXiv:1505.07131] [INSPIRE].
S.D. Mathur and D. Turton, Oscillating supertubes and neutral rotating black hole microstates, JHEP 04 (2014) 072 [arXiv:1310.1354] [INSPIRE].
R. Brustein and M. Hadad, Wave function of the quantum black hole, Phys. Lett. B 718 (2012) 653 [arXiv:1202.5273] [INSPIRE].
R. Brustein and A.J.M. Medved, Semiclassical black holes expose forbidden charges and censor divergent densities, JHEP 09 (2013) 108 [arXiv:1302.6086] [INSPIRE].
N. Itzhaki, private communication (2009).
E. Keski-Vakkuri, G. Lifschytz, S.D. Mathur and M.E. Ortiz, Breakdown of the semiclassical approximation at the black hole horizon, Phys. Rev. D 51 (1995) 1764 [hep-th/9408039] [INSPIRE].
E. Keski-Vakkuri and S.D. Mathur, Quantum gravity and turning points in the semiclassical approximation, Phys. Rev. D 54 (1996) 7391 [gr-qc/9604058] [INSPIRE].
P. Krekora, Q. Su and R. Grobe, Entanglement for pair production on the zeptosecond scale, J. Mod. Optic. 52 (2005) 489.
M.V. Fedorov, M.A. Efremov and P.A. Volkov, Double and multi-photon pair production and electron-positron entanglement, Opt. Commun. 264 (2006) 413.
T.-C. Wei, K. Nemoto, P. M. Goldbart, P.G. Kwiat, W.J. Munro and F. Verstraete, Maximal entanglement versus entropy for mixed quantum states, Phys. Rev. A 67 (2003) 022110 [quant-ph/0208138].
R. Brustein and A.J.M. Medved, Constraints on the quantum state of pairs produced by semiclassical black holes, JHEP 07 (2015) 012 [arXiv:1503.05351] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1511.05299
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Brustein, R., Medved, A.J.M. Teleporting entanglement during black hole evaporation. J. High Energ. Phys. 2016, 28 (2016). https://doi.org/10.1007/JHEP10(2016)028
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)028