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.

15 pages, 3 figures; typos corrected, references added

References in corpus (2)

• Non-Abelian Anyons and Topological Quantum Computation
• Passing through the Firewall

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