Towards bulk metric reconstruction from extremal area variations

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 b...

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Bibliographic Details
Published in:Classical and quantum gravity 2019-08, Vol.36 (18), p.185002
Main Authors: Bao, Ning, Cao, ChunJun, Fischetti, Sebastian, Keeler, Cynthia
Format: Article
Language:English
Subjects:
AdS/CFT
boundary rigidity
bulk reconstruction
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
holographic entanglement entropy
MATHEMATICS AND COMPUTING
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Summary: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.
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/ab377f