Topology of Event Horizon

TL;DR

This paper explores the possible topologies of event horizons, revealing how endpoints influence their shape and how certain topologies can be altered by choosing different timeslices, aiding understanding of their stability.

Contribution

It introduces new topological possibilities for event horizons considering endpoint existence and clarifies their relation to horizon endpoints, expanding prior smooth horizon models.

Findings

Endpoints affect event horizon topology.

Torus horizons linked to two-dimensional endpoints.

Topology can be altered by timeslicing.

Abstract

The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizons. Moreover, these aspects can be removed by an appropriate timeslicing. The result will be useful to discuss the stability and generality of the topology of the event horizon.