On the topology of stationary black holes

TL;DR

This paper proves that the domain of outer communication in certain stationary spacetimes is simply connected and that black hole horizons are topologically spherical under specific conditions.

Contribution

It establishes topological constraints on stationary black holes and their horizons, extending understanding of black hole topology in general relativity.

Findings

Domain of outer communication is simply connected.

Event horizon cross-sections are topologically spherical.

Results depend on null energy condition and additional hypotheses.

Abstract

We prove that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected. Under suitable additional hypotheses, this implies, in particular, that each connected component of a cross-section of the event horizon of a stationary black hole must have spherical topology.