On non-existence of static vacuum black holes with degenerate components of the event horizon

TL;DR

This paper provides a straightforward proof that static, vacuum black holes cannot have degenerate components on their event horizons, and discusses extensions to higher dimensions and cosmological constants.

Contribution

It offers a simple proof of the non-existence of degenerate horizon components in static vacuum black holes and explores generalizations to higher dimensions and cosmological constants.

Findings

Degenerate horizon components do not exist in static vacuum black holes.

The proof extends to higher dimensions and includes cosmological constant considerations.

Abstract

We present a simple proof of the non-existence of degenerate components of the event horizon in static, vacuum, regular, four-dimensional black hole spacetimes. We discuss the generalisation to higher dimensions and the inclusion of a cosmological constant.