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 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.