Systolic aspects of black hole entropy

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 $\mathrm{\Sigma }$ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of $\mathrm{\Sigma }$ are violated in quantum theory. We choose the systoles of $\mathrm{\Sigma }$ 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 $\mathrm{\Sigma }$. We focus on the limiting case of $\mathrm{\Sigma }$ having a large genus.