All the Stationary Vacuum States of De Sitter Space

TL;DR

This paper classifies all stationary vacuum states in de Sitter space, revealing static and rotating vacua, and explores their geometric and horizon structures, including observer-dependent horizons and ergospheres.

Contribution

It provides a complete classification of stationary vacua in de Sitter space, including new rotating solutions and their geometric properties.

Findings

Identified all stationary vacua of de Sitter space.

Discovered a family of rotating vacua and corresponding Kerr-de Sitter solutions.

Showed the existence of observer-dependent horizons and ergospheres.

Abstract

We obtain all the stationary vacua of de Sitter space by classifying the inequivalent timelike isometries of the de Sitter group. Besides the static vacuum, de Sitter space also admits a family of rotating vacua, which we use to obtain Kerr-de Sitter solutions in various dimensions. By writing the metric in a coordinate system adapted to the rotating Hamiltonian, we show that empty de Sitter space admits not only an observer-dependent horizon but also an observer-dependent ergosphere.