Towards bulk metric reconstruction from extremal area variations

doi:10.1088/1361-6382/ab377f

This content will become publicly available on August 20, 2020

Title: Towards bulk metric reconstruction from extremal area variations

Abstract

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 , 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 explicit spacetime metric reconstruction.

Authors:

Bao, Ning ^[1];

^[2];

^[3];

^[4]

Univ. of California, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Maryland, College Park, MD (United States)
McGill Univ., Montreal, QC (Canada)
Arizona State Univ., Tempe, AZ (United States)

Publication Date:: 2019-08-20

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21)

OSTI Identifier:: 1566869

Report Number(s):: BNL-212128-2019-JAAM
Journal ID: ISSN 0264-9381

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Classical and Quantum Gravity

Additional Journal Information:: Journal Volume: 36; Journal Issue: 18; Journal ID: ISSN 0264-9381

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; AdS/CFT; bulk reconstruction; holographic entanglement entropy; boundary rigidity

Citation Formats


                    Bao, Ning, Cao, ChunJun, Fischetti, Sebastian, and Keeler, Cynthia. Towards bulk metric reconstruction from extremal area variations.  United States: N. p., 2019. 
        Web.  doi:10.1088/1361-6382/ab377f.

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                    Bao, Ning, Cao, ChunJun, Fischetti, Sebastian, & Keeler, Cynthia. Towards bulk metric reconstruction from extremal area variations.  United States.  doi:10.1088/1361-6382/ab377f.

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                    Bao, Ning, Cao, ChunJun, Fischetti, Sebastian, and Keeler, Cynthia. Tue .  
        "Towards bulk metric reconstruction from extremal area variations".  United States.  doi:10.1088/1361-6382/ab377f.

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@article{osti_1566869,

  title        = {Towards bulk metric reconstruction from extremal area variations},

  author       = {Bao, Ning and Cao, ChunJun and Fischetti, Sebastian and Keeler, Cynthia},

  abstractNote = {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 , 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 explicit spacetime metric reconstruction.},

  doi          = {10.1088/1361-6382/ab377f},

  journal      = {Classical and Quantum Gravity},

  number       = 18,

  volume       = 36,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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Journal Article:

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This content will become publicly available on August 20, 2020

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DOI: 10.1088/1361-6382/ab377f

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