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Towards bulk metric reconstruction from extremal area variations

Bao, Ning and Cao, ChunJun and Fischetti, Sebastian and Keeler, Cynthia (2019) Towards bulk metric reconstruction from extremal area variations. Classical and Quantum Gravity, 36 (18). Art. No. 185002. ISSN 0264-9381. doi:10.1088/1361-6382/ab377f.

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The Ryu–Takayanagi and Hubeny–Rangamani–Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ⩾ 4, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicitspacetime metric reconstruction.

Item Type:Article
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URLURL TypeDescription Paper
Bao, Ning0000-0002-3296-1039
Cao, ChunJun0000-0002-5761-5474
Fischetti, Sebastian0000-0002-2783-211X
Keeler, Cynthia0000-0002-4248-3704
Additional Information:© 2019 IOP Publishing Ltd. Received 23 April 2019; Accepted 31 July 2019; Accepted Manuscript online 31 July 2019; Published 20 August 2019. We thank Spyridon Alexakis, Xi Dong, Netta Engelhardt, Nikolaos Eptaminitakis, Daniel Harlow, Gary Horowitz, Robin Graham, Daniel Kabat, Sorin Mardare, Reed Meyerson, and Matteo Santacesaria for useful and interesting conversations while this work was being completed; we are especially grateful to Tracey Balehowsky for her patience in explaining her work [48] to us and to Gunther Uhlmann for extensive discussions regarding inverse boundary value problems. CC would also like to thank Gunther Uhlmann for his helpful suggestions and his hospitality during the visits to the University of Washington. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958; in particular, NB, SF, and CK would like to thank both the KITP and OIST for hospitality during the completion of a portion of this work. NB is supported by the National Science Foundation under Grant No. 82248-13067-44-PHPXH, by the Department of Energy under Grant No. DE-SC0019380, and by New York State Urban Development Corporation Empire State Development contract no. AA289. CC acknowledges the support by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, as well as by the US Department of Defense and NIST through the Hartree Postdoctoral Fellowship at QuICS. SF acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN/00032-2015. The work of CK is supported by the US Department of Energy under Grant No. DE-SC0019470. This work was supported in part by a grant from the Simons Foundation (385602, AM).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0019380
New York State Urban Development Corporation Empire State DevelopmentAA289
Department of Energy (DOE)DE-SC0011632
Department of DefenseUNSPECIFIED
National Institute of Standards and Technology (NIST)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)SAPIN/00032-2015
Department of Energy (DOE)DE-SC0019470
Simons Foundation385602
Issue or Number:18
Record Number:CaltechAUTHORS:20190820-131613485
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Official Citation:Ning Bao et al 2019 Class. Quantum Grav. 36 185002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98040
Deposited By: Tony Diaz
Deposited On:20 Aug 2019 21:10
Last Modified:12 Jul 2022 19:45

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