Towards bulk metric reconstruction from extremal area variations

Bao, Ning; Cao, ChunJun; Fischetti, Sebastian; Keeler, Cynthia

doi:10.1088/1361-6382/ab377f

Title: Towards bulk metric reconstruction from extremal area variations

Journal Article · 19 August 2019 · Classical and Quantum Gravity

DOI: https://doi.org/10.1088/1361-6382/ab377f · OSTI ID:1566869

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)

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.

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Research Organization:: Arizona State Univ., Tempe, AZ (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0012704; SC0019470

OSTI ID:: 1566869

Report Number(s):: BNL--212128-2019-JAAM

Journal Information:: Classical and Quantum Gravity, Journal Name: Classical and Quantum Gravity Journal Issue: 18 Vol. 36; ISSN 0264-9381

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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