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.

11 pages. No figures. LaTeX2e. Final form, to be published in the Int. J. Geom. Methods Mod. Physics

References in corpus (2)

• Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry
• Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics