Islands outside the horizon

By Ahmed Almheiri, R. Mahajan, J. Maldacena. 2019

309 citations recorded by the source corpus.

We consider an AdS$_2$ black hole in equilibrium with a bath, which we take to have a dual description as (0+1)-dimensional quantum mechanical system coupled to a (1+1)-dimensional field theory serving as the bath. We compute the entropies of both the quantum mechanical degrees of freedom and of the bath separately, while allowing contributions from entanglement wedge "islands". We find situations where the island extends {\it outside} the black hole horizon. This suggests possible causality paradoxes which we show are avoided because of the quantum focusing conjecture. Finally, we formulate a version of the information paradox for a black hole in contact with a bath in the Hartle-Hawking state, and demonstrate the role of islands in resolving this paradox.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b4ec63a7c8cd2c5fdba6ae887cbc9904d3dc7d56

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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 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. A. Karch

In Statistical and Nonlinear Physics

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

Citations in the corpus

• 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 flow in black hole evaporation (2019, unknown): “Here we will focus on the second of these, which See also the important follow-up discussions of [3, 14–16].”
• Islands in asymptotically flat 2D gravity (2020, background): “an the evaporating black hole, the late time behavior of the quantum extremal surfaces in the evaporating black hole is well-approximated by those in the eternal black hole. Moreover, as discussed in [43,54,55], the eternal black hole furnishes a 22 Figure 7: Island in the eternal black hole. With t”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “In particular, we study eternal black holes coming to equilibrium with an external heat bath (prepared at the same temperature) in a higher dimensional analog of the analysis appearing in [23].”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “{115]). The exact location and nature of the above non-local interactions is clearly 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 t”
• Notes on islands in asymptotically flat 2d dilaton black holes (2020, methodology): “In this case, the leading term of this von Neumann entropy of the CFT matter can be well approximated and given by twice of the one in the single interval on the right side [13],”
• Replica wormholes and the entropy of Hawking radiation (2019, methodology): “gion is coupled to JT gravity. In a unitary theory, S R(t) should saturate at around the twice the Bekenstein-Hawking entropy of each black hole, see gure5. This was conrmed using the island rule in [14]. 1.3 Replica wormholes to the rescue To reproduce the unitary answer directly from a gravity cal”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “For the two dimensional bulk gravity case, we summarize the setup of [2], describe the connection to our model and introduce eternal black holes.”
• Islands in cosmology (2020, background): “ quantum apparent horizon. For eternal black holes, the quantum apparent horizon is the same as the event horizon, so it follows that the island ends outside (or on) the event horizon, as observed in [32,33]. For evaporating black holes, the quantum apparent horizon is inside the event horizon, and ”
• Inconsistency of islands in theories with long-range gravity (2021, methodology): “4 The island rule [1,38] then provides a method of deriving the entanglement entropy of a region, R, in the non-gravitational system.”
• Replica wormholes and the black hole interior (2019, methodology): “For other recent work on this topic, see [17, 18, 19, 20, 21, 22].”
• Lessons from the information paradox (2020, background): “d a dual description as a black hole then in the picture of Figure22, it looks like radiation from the black hole is entering the bath and crossing the imaginary interface, I. This is the reason that [8,118] { 74 { termed the subsystem to the left the \black hole" and the subsystem to the right”
• Entanglement islands in higher dimensions (2019, background): “s, it wins at late times. Overall, we get an entropy that grows linearly and then saturates. This also means that the entanglement wedge of the union of the two baths contains an island at late times [15]. In gure5, this island is the region on the left vertical edge between the two points where the”
• Information Transfer with a Gravitating Bath (2020, background): “This is exactly the recent story of entanglement islands in the KR braneworld that gives a Page curve resolving a version of the information paradox for the eternal black hole [8].”
• Bra-ket wormholes in gravitationally prepared states (2020, methodology): “ c e-foldings, the paradox will likely occur independently of the initial conditions for in ation. 40 a compact spatial slice, see gure18(c). So this setup is rather similar to the one considered in [26], and we therefore expect islands in the interior of these black holes. Indeed, we can make an an”
• The Holographic Nature of Null Infinity (2020, result): “g aside this question of interpretation, out results are not in contradiction with those of [5,6,7] since their setting is dierent. The Page curve in at space? On the other hand, it was suggested in [52] that the setup of Figure4bmay have \phenomenological" applications in that the entropy of t”