The Page curve of Hawking radiation from semiclassical geometry
By Ahmed Almheiri, R. Mahajan, J. Maldacena, Ying Zhao. Journal of High Energy Physics, 2019
715 citations recorded by the source corpus.
We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for “islands” in determining the entanglement wedge.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c3769b361465a91e8a7eac33a2432fb3450af1d
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Citations in the corpus
- Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “ntities allowed by our formalism include quantities that in a dual CFT would describe matrix elements of operators as well as e.g. Trˆn for a wide variety of density matrices. The Renyi entropies of [44,49] are { 3 { then functions of these quantities. In accordwith the original works [55{57], our a”
- Islands in de Sitter space (2020, methodology): “ntangling system while also having zero boundary area. Thus, at rst glance, the island formula seems to be saying that the entropy of an auxiliary system entangled with a closed universe must be zero [1]. But this conclusion poses several conceptual diculties. For example, in the G N !0 limit where ”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “enario considered in [2]. The key feature of our holographic model [1] is that it reproduces the three de{ 4 { scriptions of the underlying physics discussed above for the doubly-holographic model of [15]. From the boundary perspective, our system consists of a d-dimensional holographic CFT coupled ”
- Islands outside the horizon (2019, background): “2 Since the theory under consideration is conformal, we can do the OPE expansion (in the (1)Unlike [3], in this paper, we do not demand that the CFT2 has a three-dimensional holographic dual.”
- Notes on islands in asymptotically flat 2d dilaton black holes (2020, background): “ gravity as holographic description, are expected to play an important role. Recently, the idea called island was proposed to explain the unitary Page curve in the bulk [5{7]. The proposed formula in [7] for the \quantum" entanglement entropy of the thermal radiation is S R= min ˆ ext A[@I] 4G”
- Information flow in black hole evaporation (2019, methodology): “after a quantum quench, wherein the holographic theory and the bath are joined. One particularly exciting development is the appearance of ‘ER=EPR’-like wormholes in the (doubly) holographic model of [3]. At late times, the entanglement wedge of the bath includes the interior of the black hole. In t”
- Information radiation in BCFT models of black holes (2019, background): “e. C) The Planck-brane picture suggests an eective lower-dimensional description where a part of the CFT in the central region is replaced with a cuto CFT coupled to gravity, similar to the setup in [3]. for calculating these entropies in the gravity picture requires the identication of a \quantum e”
- 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.”
- Entanglement islands in higher dimensions (2019, methodology): “Since this is a very hard problem, we have made the simplification that the matter CFT4 has a 5d holographic dual, as in [14], and so the 4d quantum extremal surfaces become ordinary 5d RT surfaces.”
- Replica wormholes and the black hole interior (2019, background): “This idea was given an elegant “doubly holographic” realization in [16], where it was called the “island conjecture.”
- Islands in cosmology (2020, methodology): “This may provide another way to analyze this model along the lines of [13,64–67], but we will not take this perspective.”
- Page curve for an evaporating black hole (2020, methodology): “In the gravitational theory the Hawking 2More precisely, the island refers to the internal entanglement wedge defined by I [11].”
- 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)”
- Lessons from the information paradox (2020, methodology): “Some of the initial computations of the Page curve [7, 8, 118] were performed in 1 + 1 dimensions, and the framework was later generalized to higher dimensions [119].”
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “In any event, this more or less standard holographic model can be viewed from three perspectives in analogy with [22]: the bulk gravity perspective, with a brane coupled to gravity in an asymptotically AdSd+1 space; the boundary perspective, with the boundary CFT coupled to a conformal defect; and t”
- Bra-ket wormholes in gravitationally prepared states (2020, background): “To gain some further intuition, we can consider the “doubly holographic” set up introduced in [36].”