Entanglement wedge reconstruction and the information paradox

By Geoffrey Penington. Journal of High Energy Physics, 2019

929 citations recorded by the source corpus.

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2πlogSBH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5e13a5954ece712832ff094719e0603f908af95b

How researchers see this paper

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In Astronomy and Astrophysics

1. S. Raju
2. D. Stanford
3. R. Myers
4. J. Maldacena
5. D. Harlow
6. S. Shenker
7. Thomas Hartman
8. L. Susskind

In Atomic and Molecular Physics, and Optics

1. S. Raju
2. D. Stanford
3. R. Myers
4. J. Maldacena
5. S. Shenker
6. Ahmed Almheiri
7. H. Chen
8. Zhenbin Yang

In Nuclear and High Energy Physics

1. S. Raju
2. R. Myers
3. D. Stanford
4. J. Maldacena
5. D. Harlow
6. S. Shenker
7. Thomas Hartman
8. H. Chen

Citations in the corpus

• Information flow in black hole evaporation (2019, background): “This novel transition occurs in this holographic model (and in the model described by [1]) as a result of the existence of a new class of QESs just inside the event horizon of the evaporating black hole.”
• Islands in asymptotically flat 2D gravity (2020, methodology): “e black hole entropy is equal to the radiation entropy after 1/3rd of the black hole evaporates. 3.4 Scrambling time We now compute the scrambling time associated to the island rule entropy following [2,3]. The scrambling time is the time it takes for information dropped into a black hole to reappea”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, methodology): “learly of some interest. In particular, while quantum extremal surfaces may appear outside the black hole’s event horizon [45], for black holes evaporating into a vacuum they should always lie inside [42,43]. Were all of the physics determined by replica wormholes conned far enough inside the horizo”
• Massive islands (2020, methodology): “One key insight in the calculation of the Page curve in [3, 4] is that the true quantum entangling surface jumps in the process of black hole evaporation.”
• The Holographic Nature of Null Infinity (2020, background): “ge curve is best understood purely on the boundary: it is the standard Page curve of the boundary quantum eld theory as energy in one region (D) spreads into the surrounding region (C). The setups of [5,6,7] are all essentially of this type, and one setup is displayed in4b. In all of them, we couple”
• Islands in Schwarzschild black holes (2020, background): “So far, among recent works [5–8, 12, 13, 17–27], the island rule has been studied mainly in two spacetime dimensions,1 which offer a tractable treatment of the entanglement entropy of the Hawking radiation.”
• Information Transfer with a Gravitating Bath (2020, methodology): “In the description (II), using the quantum corrected RyuTakayanagi formula [52–54], this is given by the so-called island rule [1,27] as, S(R) =min ext I Sgen(R∪ I), (1)”
• Entanglement islands in higher dimensions (2019, background): “4 of [12], where an argument using the intermediate value theorem was presented for the existence of a quantum extremal surface behind the horizon.”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “The early work of [21] considered black hole evaporation with Einstein gravity in higher dimensions, and the holographic model of [22] was extended to a holographic framework with d = 4 in [24] using numerical calculations.”
• Lessons from the information paradox (2020, result): “The physical effect above — that degrees of freedom that appear to belong to one region may have a redundant description in terms of degrees of freedom in another region — is similar to the “island phenomenon” that has received significant recent attention [6–9].”
• Replica wormholes and the black hole interior (2019, methodology): “This is consistent with the lower bounds on the reconstruction error derived in [13, 14].”
• The Page curve of Hawking radiation from semiclassical geometry (2019, background): “Progress on a direct derivation of (15) has been reported in [46,47].”
• Inconsistency of islands in theories with long-range gravity (2021, methodology): “4 The island rule [1, 80] then provides a method of deriving the entanglement entropy of a region, R, in the non-gravitational system.”
• Page curve for an evaporating black hole (2020, methodology): “We follow the holographic approach of [4, 5], which uses the quantum Ryu-Takayanagi (QRT) formula”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “es; see e.g. [25,26] for recent reviews and [24] for further recent discussion. { 3 { Note to reader: While this work was underway we learned that related results were independently found in the work [27] which will appear on the arxiv simultaneously. 1.1 Holographic Hayden-Preskill Before proceedin”
• Replica wormholes and the entropy of Hawking radiation (2019, methodology): “For example, we could imagine an AdS/CFT example that involves an extremal black hole such that it also has a CFT on its geometry.”