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

摘要

The crease set of an event horizon or a Cauchy horizon is an important objectwhich determines qualitative properties of the horizon. In particular, itdetermines the possible topologies of the spatial sections of the horizon. ByFermat's principle in geometric optics, we relate the crease set and theMaxwell set of a smooth function in the context of singularity theory. Wethereby give a classification of generic topological structure of the Maxwellsets and the generic topologies of the spatial section of the horizon.