Further restrictions on the topology of stationary black holes in five dimensions

TL;DR

This paper constrains the possible topologies of stationary black hole horizons in five dimensions, showing they can be composed of specific manifolds like Lens spaces, handles, and quotients of spheres, without assuming extra symmetries.

Contribution

It provides new restrictions on horizon topologies in 5D black holes, including classifications involving Lens spaces, handles, and quotients of spheres, without additional Killing vector assumptions.

Findings

Horizon manifold can be a connected sum of Lens spaces and handles or a quotient of S^3.

The topology of the domain of outer communication is a product of time with a connected sum of specific 4-manifolds.

Black hole horizon topologies include Prism manifolds and quotients of the Poincare homology sphere.

Abstract

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.