Paper detail

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