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Entanglement Entropy of Black Holes

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 regul...

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Autor principal: Solodukhin, Sergey N.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2011
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255889/
https://www.ncbi.nlm.nih.gov/pubmed/28179833
http://dx.doi.org/10.12942/lrr-2011-8
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author Solodukhin, Sergey N.
author_facet Solodukhin, Sergey N.
author_sort Solodukhin, Sergey N.
collection PubMed
description 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 blackhole 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.
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spelling pubmed-52558892017-02-06 Entanglement Entropy of Black Holes Solodukhin, Sergey N. Living Rev Relativ Review Article 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 blackhole 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. Springer International Publishing 2011-10-21 2011 /pmc/articles/PMC5255889/ /pubmed/28179833 http://dx.doi.org/10.12942/lrr-2011-8 Text en © The Author(s) 2011
spellingShingle Review Article
Solodukhin, Sergey N.
Entanglement Entropy of Black Holes
title Entanglement Entropy of Black Holes
title_full Entanglement Entropy of Black Holes
title_fullStr Entanglement Entropy of Black Holes
title_full_unstemmed Entanglement Entropy of Black Holes
title_short Entanglement Entropy of Black Holes
title_sort entanglement entropy of black holes
topic Review Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255889/
https://www.ncbi.nlm.nih.gov/pubmed/28179833
http://dx.doi.org/10.12942/lrr-2011-8
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