Non-existence of toroidal cohomogeneity-1 near horizon geometries

TL;DR

This paper proves that certain higher-dimensional stationary near horizon geometries with specific symmetries cannot have toroidal topology, extending known results to include a cosmological constant.

Contribution

It establishes the non-existence of toroidal horizon topologies for a broad class of near horizon geometries in higher dimensions, including the presence of a cosmological constant.

Findings

Toroidal horizon topologies are impossible in D≥5 stationary, non-static near horizon geometries with (D-3) rotational symmetries.

In D=4, the same non-existence result holds with a non-negative cosmological constant.

The proof extends previous classifications by including cosmological constant effects.

Abstract

We prove that $D\geq 5$ dimensional stationary, non-static near horizon geometries with (D-3) rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D=4 dimensions the same result is obtained under the assumption of a non-negative cosmological constant.