2014/08/31 by Matthew Headrick, Robert C. Myers, Jason Wien · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep10(2014)149
published as JHEP 10: 149 (2014) · 62 pages; v2: minor improvements to presentation, references added
arxiv created 2014/11/11 · arxiv updated 2015/06/22
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.