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The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

Journal of High Energy Physics volume 2019, Article number: 63 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

Bulk quantum fields are often said to contribute to the generalized entropy \( \frac{A}{4{G}_N}+{S}_{\mathrm{bulk}} \) 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 \( \frac{\beta }{2\pi}\log \varDelta S+O(1) \) 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.

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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Ahmed Almheiri

  2. Department of Physics, Princeton University, Princeton, NJ, 08544, USA

    Netta Engelhardt

  3. Gravity Initiative, Princeton University, Princeton, NJ, 08544, USA

    Netta Engelhardt

  4. Physics Department, University of California, Santa Barbara, CA, 93016, USA

    Donald Marolf & Henry Maxfield

Authors
  1. Ahmed Almheiri
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  2. Netta Engelhardt
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Correspondence to Netta Engelhardt.

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ArXiv ePrint: 1905.08762

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Almheiri, A., Engelhardt, N., Marolf, D. et al. The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. J. High Energ. Phys. 2019, 63 (2019). https://doi.org/10.1007/JHEP12(2019)063

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  • DOI: https://doi.org/10.1007/JHEP12(2019)063

Keywords

  • 2D Gravity
  • AdS-CFT Correspondence
  • Black Holes in String Theory
  • Gauge- gravity correspondence