Gautam Satishchandran - Black hole entropy is von Neumann entropy

In this talk, I will show that the algebra of observables in the “exterior” of any Killing horizon always contains a Type II factor "localized" on the horizon and, consequently, the entropy of semi-classical states is the generalized entropy. I will illustrate this with two examples of (1) a black hole in asymptotically flat spacetime and (2) black holes in asymptotically de Sitter. In all cases, the von Neumann entropy for semiclassical states is given by the generalized entropy.

More generally, our results suggest that in all cases where there exists another "boundary structure" (e.g., an asymptotic boundary or another Killing horizon) the algebra of observables has no maximum entropy state and in the absence of such structures (e.g., de Sitter) the algebra contains a maximum entropy state.