Geometric secret sharing in a model of Hawking radiation

Journal Article · Wed Jan 27 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2021)177· OSTI ID:1849604

Balasubramanian, Vijay ^[1]; Kar, Arjun ^[2]; Parrikar, Onkar ^[3]; Sárosi, Gábor ^[4]; Ugajin, Tomonori ^[2]

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1. Univ. of Pennsylvania, Philadelphia, PA (United States). David Rittenhouse Lab.; Vrije Univ. Brussels (Belgium) . International Solway Inst. Theoretische Natruurkunde; Univ. of Pennsylvania, Philadelphia, PA (United States)
2. Univ. of Pennsylvania, Philadelphia, PA (United States). David Rittenhouse Lab.
3. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
4. European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.

We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

• Research Organization: Duke Univ., Durham, NC (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)
• Sponsoring Organization: Simons Foundation; USDOE Office of Science (SC)
• Grant/Contract Number: FG02-05ER41367; SC0013528; SC0020360
• OSTI ID: 1849604
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2021; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
AdS-CFT correspondence
Black holes
Physics