On the mass of static metrics with positive cosmological constant - I

TL;DR

This paper introduces a new concept of mass for static metrics with positive cosmological constant, characterizes the de Sitter solution uniquely, and extends the analysis to negative cosmological constant, establishing a uniqueness theorem for Anti de Sitter spacetime.

Contribution

It proposes a novel notion of mass for static metrics with positive cosmological constant and proves uniqueness results for de Sitter and Anti de Sitter spacetimes.

Findings

De Sitter solution characterized as the only static vacuum with zero mass.

New notion of mass for compact static metrics with positive cosmological constant.

Uniqueness theorem for Anti de Sitter spacetime with negative cosmological constant.

Abstract

In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leading to a uniqueness theorem for the Anti de Sitter spacetime.