Bekenstein-Hawking Entropy as Topological Entanglement Entropy
Abstract
Black holes in 2+1 dimensions enjoy long range topological interactions similar to those of non-abelian anyon excitations in a topologically ordered medium. Using this observation, we compute the topological entanglement entropy of BTZ black holes, via the established formula S_top = log(S^a_0), with S_b^a the modular S-matrix of the Virasoro characters chi_a(tau). We find a precise match with the Bekenstein-Hawking entropy. This result adds a new twist to the relationship between quantum entanglement and the interior geometry of black holes. We generalize our result to higher spin black holes, and again find a detailed match. We comment on a possible alternative interpretation of our result in terms of boundary entropy.
Keywords
Cite
@article{arxiv.1308.2342,
title = {Bekenstein-Hawking Entropy as Topological Entanglement Entropy},
author = {Lauren McGough and Herman Verlinde},
journal= {arXiv preprint arXiv:1308.2342},
year = {2015}
}
Comments
15 pages, 3 figures; typos corrected, references added