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Holographic holes and differential entropy

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  • Published: 27 October 2014
  • Volume 2014, article number 149, (2014)
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Holographic holes and differential entropy
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  • Matthew Headrick1,
  • Robert C. Myers2 &
  • Jason Wien2,3 

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A preprint version of the article is available at arXiv.

Abstract

Recently it has been shown 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 [1, 2]. 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.

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Authors and Affiliations

  1. Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts, 02453, United Kingdom

    Matthew Headrick

  2. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Robert C. Myers & Jason Wien

  3. Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Jason Wien

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  1. Matthew Headrick
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Correspondence to Robert C. Myers.

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ArXiv ePrint: 1408.4770

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Headrick, M., Myers, R.C. & Wien, J. Holographic holes and differential entropy. J. High Energ. Phys. 2014, 149 (2014). https://doi.org/10.1007/JHEP10(2014)149

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  • Received: 28 August 2014

  • Accepted: 13 October 2014

  • Published: 27 October 2014

  • DOI: https://doi.org/10.1007/JHEP10(2014)149

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Keywords

  • Gauge-gravity correspondence
  • AdS-CFT Correspondence
  • Models of Quantum Gravity
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