Bekenstein-Hawking Entropy as Topological Entanglement Entropy

TL;DR

This paper demonstrates that the topological entanglement entropy of 2+1 dimensional black holes matches the Bekenstein-Hawking entropy, revealing a deep connection between quantum entanglement and black hole geometry.

Contribution

It establishes a precise correspondence between topological entanglement entropy and black hole entropy, extending the analysis to higher spin black holes.

Findings

Topological entanglement entropy matches Bekenstein-Hawking entropy.

The result applies to higher spin black holes with detailed agreement.

Suggests a boundary entropy interpretation of black hole 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.