Bekenstein-Hawking Entropy as Topological Entanglement Entropy

Understand

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.