Vol. 14 (2011) > lrr-2011-8

doi: 10.12942/lrr-2011-8
Living Rev. Relativity 14 (2011), 8

Entanglement Entropy of Black Holes

1 Laboratoire de Mathématiques et Physique Théorique, Université François-Rabelais Tours Fédération Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours, France

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Article Abstract

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

Keywords: black holes, Bekenstein-Hawking entropy, entanglement entropy

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Sergey N. Solodukhin,
"Entanglement Entropy of Black Holes",
Living Rev. Relativity 14,  (2011),  8. URL (cited on <date>):

Article History

ORIGINAL http://www.livingreviews.org/lrr-2011-8
Title Entanglement Entropy of Black Holes
Author Sergey N. Solodukhin
Date accepted 23 August 2011, published 21 October 2011
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