Systolic aspects of black hole entropy

Abstract

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3+1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections $\Sigma$ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of $\Sigma$ are violated in quantum theory. We choose the systoles of $\Sigma$ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of $\Sigma$. We focus on the limiting case of $\Sigma$ having a large genus.