Stable Topologies of Event Horizon

TL;DR

This paper investigates the stability of event horizon topologies, revealing that simple spherical horizons are unstable while more complex, handle-like topologies are structurally stable, with implications for understanding black hole mergers.

Contribution

It demonstrates the stability properties of event horizon topologies, especially showing that handle-like horizons are structurally stable, extending previous work on horizon endpoints.

Findings

Single spherical EH is unstable.

EHs with handles are structurally stable.

Topology changes are linked to endpoints of the EH.

Abstract

In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.