The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
By Ahmed Almheiri, Netta Engelhardt, D. Marolf, Henry Maxfield. Journal of High Energy Physics, 2019
874 citations recorded by the source corpus.
Bulk quantum fields are often said to contribute to the generalized entropy A4GN+Sbulk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{A}{4{G}_N}+{S}_{\mathrm{bulk}} $$\end{document} only at O(1). Nonetheless, in the context of evaporating black holes, O(1/GN ) gradients in Sbulk can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary 2d bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time β2πlogΔS+O1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\beta }{2\pi}\log \varDelta S+O(1) $$\end{document} in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b1605237c94039cc8f1264b7d8c5d94abc673a54
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Citations in the corpus
- Replica wormholes and the black hole interior (2019, methodology): “As argued in [14, 15], this can be addressed using entanglement wedge reconstruction.”
- Notes on islands in asymptotically flat 2d dilaton black holes (2020, background): “Recently, the idea called island was proposed to explain the unitary Page curve in the bulk [5–7].”
- Islands outside the horizon (2019, methodology): “Of course this is the same idea as was described in [1, 2].”
- Entanglement wedge reconstruction and the information paradox (2019, methodology): “After the completion of this manuscript, the author became aware of independent related work by Almheiri, Engelhardt, Marolf and Maxfield [43], which was published simultaneously.”
- Information flow in black hole evaporation (2019, methodology): “This two-dimensional model [2] was then extended with an extra layer of holography by [3].”
- Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, methodology): “In particular, under very general conditions [42, 43] argued that one could obtain this result by computing the generalized entropy Sgen = A 4G + Sbulk of an appropriate comdimension-2 quantum extremal surface (QES) , where the surface is chosen so that holography suggests this might represent Srad.”
- Lessons from the information paradox (2020, methodology): “Consider a theory of gravity in a d-dimensional asymptotically AdS spacetime, where the matter content itself is that of a holographic CFT [120].”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “, [2, 13, 15, 113]).”
- Islands in cosmology (2020, background): “The lower bound was obtained in [11] as follows.”
- Massive islands (2020, methodology): “Of course many of the explicit Page curve calculations have been done in low dimensional systems [4, 16].”
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “In [20], Φ̃0 would also absorb a logarithmic constant −2 log(L/zB), which would be accompanied by a shift in the prefactor in the argument of the logarithmic term in eq.”
- Information Transfer with a Gravitating Bath (2020, background): “An important and interesting advance in our understanding of the quantum mechanics of black holes is the set of recent calculations [1, 2] of the time evolution of the entanglement entropy between a holographic system that contains a black hole and an external bath.”
- Entanglement islands in higher dimensions (2019, background): “The papers [12,13] considered the coupling of a large AdS black hole to a flat space bath region, allowing the black hole to evaporate.”