Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant

TL;DR

This paper proves that de Sitter spacetime is uniquely characterized among static vacua with positive cosmological constant by properties of its Killing horizons, extending previous uniqueness theorems to more general cases.

Contribution

It extends the uniqueness theorems for de Sitter spacetime to include more general horizon metrics and multiple horizons.

Findings

de Sitter spacetime has minimal Dirac operator modes on its horizons

de Sitter is the only vacuum with horizon metrics at least that of a round sphere

extends previous uniqueness theorems to broader horizon conditions

Abstract

We prove that, among all (n + 1)-dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing hori-zons have minimal modes for the Dirac operator. As a consequence, the de Sitter spacetime is the only vacuum of this type for which the induced metric tensor on some of its Killing horizons is at least equal to that of a round (n -- 1)-sphere. This extends unique-ness theorems shown by Boucher-Gibbons-Horowitz and Chruciel to more general horizon metrics and to the non-single horizon case.