Holographic holes and differential entropy
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Publication:271196
DOI10.1007/JHEP10(2014)149zbMATH Open1333.83189arXiv1408.4770MaRDI QIDQ271196
Author name not available (Why is that?)
Publication date: 7 April 2016
Published in: (Search for Journal in Brave)
Abstract: Recently, it has been shown by Balasubramanian et al. and Myers et al. that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.
Full work available at URL: https://arxiv.org/abs/1408.4770
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