Static Black Hole Uniqueness for nonpositive masses

TL;DR

This paper provides a simpler proof of the static uniqueness of Kottler spacetimes with nonpositive mass, extending the understanding of black hole solutions in negative cosmological constant settings.

Contribution

It offers an elementary alternative proof of the static uniqueness theorem and discusses potential generalizations to degenerate horizons.

Findings

Simplified proof of static uniqueness for Kottler spacetimes

Extension to degenerate horizons discussed

Connections to Penrose inequality for negative cosmological constant

Abstract

In arXiv:1310.3002, Lee and Neves proved a Penrose inequality for spacetimes with negative cosmological constant and nonpositive mass aspect. As an application, they were able to obtain a static uniqueness theorem for Kottler spacetimes with nonpositive mass. In this paper, we propose an alternative more elementary proof of this static uniqueness result and we discuss some possible generalizations, most notably to degenerate horizons.