Topological classification of black Hole: Generic Maxwell set and crease set of horizon

TL;DR

This paper classifies the generic topological structures of Maxwell sets and horizon spatial sections using singularity theory, linking geometric optics principles to horizon topology in black hole physics.

Contribution

It introduces a novel classification framework for horizon topologies based on the Maxwell set and crease set analysis, connecting geometric optics and singularity theory.

Findings

Classification of generic Maxwell set topologies

Determination of horizon spatial section topologies

Linking crease set structure to horizon properties

Abstract

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.