Embolic aspects of black hole entropy

Abstract

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3+1)-dimensional spacetimes. We treat the case of horizons having space-like sections $\Sigma$ which are topological spheres, following Hawking's and the Topological Censorship theorems. We use the injectivity radius of the induced metric on $\Sigma$ to encode the linear dimensions of the elementary cells giving rise to such entropy. We use the topological entropy of $\Sigma$ as the fundamental quantity expressing the complexity of $\Sigma$ on which its entropy depends. We point out the significance, in this context, of the Berger and Croke isoembolic inequalities.