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:
-
- 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:
- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States); Arizona State Univ., Tempe, AZ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1566869
- Alternate Identifier(s):
- OSTI ID: 1597022
- Report Number(s):
- BNL-212128-2019-JAAM
Journal ID: ISSN 0264-9381; TRN: US2001006
- Grant/Contract Number:
- SC0012704; SC0019470
- 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
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.
Bao, Ning, Cao, ChunJun, Fischetti, Sebastian, & Keeler, Cynthia. Towards bulk metric reconstruction from extremal area variations. United States. doi:10.1088/1361-6382/ab377f.
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. https://www.osti.gov/servlets/purl/1566869.
@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}
}
Web of Science
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