Systolic Aspects of Black Hole Entropy - Nikolaos Kalogeropoulos (Axioms, 2020)
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 <semantics> Σ </semantics> of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of <semantics> Σ </semantics> are violated in quantum theory. We choose the systoles of <semantics> Σ </semantics> 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 <semantics> Σ </semantics> . We focus on the limiting case of <semantics> Σ </semantics> having a large genus.