Replica wormholes and the entropy of Hawking radiation
By Ahmed Almheiri, Thomas Hartman, J. Maldacena, Edgar Shaghoulian, Amirhossein Tajdini. Journal of High Energy Physics, 2019
775 citations recorded by the source corpus.
The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number n → 1, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f907ad36588ed8b64e40f6bd101653325d1b1453
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Citations in the corpus
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “See also [20, 23, 25, 26, 29].”
- Replica wormholes and the black hole interior (2019, methodology): “Closely related work has been done independently by Ahmed Almheiri, Tom Hartman, Juan Maldacena, Edgar Shaghoulian and Amirhossein Tajdini [49].”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “In the two-dimensional models involving JT gravity studied so far [39, 41], the existence of wormholes follows from the fact that JT gravity is defined by averaging over an ensemble of Hamiltonians.”
- Islands in cosmology (2020, methodology): “Recent developments in the study of the black hole information paradox [11–15] have led to a new interpretation of the black hole interior that depends, crucially, on the apparent violation of (1.”
- Lessons from the information paradox (2020, methodology): “Then, in d = 1, it is possible to carefully compute the entanglement entropy of R using the replica trick in the Euclidean path integral [7, 9].”
- Notes on islands in asymptotically flat 2d dilaton black holes (2020, background): “The emergence of islands are also shown by the replica trick in the JackiwTeitelboim (JT) gravity in [14, 15].”
- Inconsistency of islands in theories with long-range gravity (2021, methodology): “1) has been carefully derived in JT gravity using a replica trick [4].”
- Islands in de Sitter space (2020, methodology): “ation of this formula, the naive eective eld theory calculation of the radiation entropy is corrected by a non-perturbative gravitational eect: Euclidean wormholes which appear in the replica trick [9,10]. Such wormholes provide additional saddle-points for the gravitational path integral used to co”
- Information Transfer with a Gravitating Bath (2020, background): “crucial ingredient in this calculation is the appearance of entanglement islands [7–10], which are seemingly disconnected parts in the holographic system that contribute to the entanglement entropy of a region of the bath.”
- Information radiation in BCFT models of black holes (2019, methodology): “The observations of this section relating the entanglement wedge phase transition and the appearance of connected boundary saddles were directly inspired by similar observations in the JT-gravity context [50]; related obnservations were made independently by [51].”
- 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.”
- Massive islands (2020, methodology): “Most of the work on islands has been done in lower dimensions [16, 18, 19].”
- Bra-ket wormholes in gravitationally prepared states (2020, methodology): “Computing the entropy using the replica trick, this formula is derived from the existence of replica wormholes [7,8], which in turn can be viewed as the result of inserting extra twist operators in the gravitational region.”
- 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”
- Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “uch entropies will then reproduce an appropriate Page curve dened by the Bekenstein-Hawking entropy. In particular, the nal result will then be much as in the recent discussions of replica wormholes [48,49] which in our language are indeed the most natural saddle points contributing to the average e”