Systolic aspects of black hole entropy

TL;DR

This paper explores a mesoscopic topological approach to black hole entropy, linking it to the complexity of the horizon's spatial sections and their systolic geometry, especially for high-genus surfaces.

Contribution

It introduces a novel topological perspective on black hole entropy by relating it to the systolic geometry of horizon sections, emphasizing quantum violations of classical energy conditions.

Findings

Entropy related to the topology of horizon slices

Systoles encode the complexity of spatial sections

Large genus surfaces influence entropy calculations

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.