Embolic 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 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.