Simultaneous baldness and cosmic baldness and Kottler spacetime

TL;DR

This paper proves a no-hair theorem for the Kottler spacetime, showing its uniqueness and stability in the presence of imperfect fluids, and clarifies the solution's distinctness from alternatives.

Contribution

It establishes a simultaneous no-hair and cosmic no-hair theorem for the Kottler spacetime with imperfect fluids, confirming its uniqueness among solutions.

Findings

Proves the uniqueness of the Kottler/Schwarzschild-de Sitter solution.

Shows alternatives are either different solutions or disguised versions.

Demonstrates a no-hair theorem in the presence of imperfect fluids.

Abstract

The uniqueness of the Kottler/Schwarzschild-de Sitter solution of the vacuum Einstein equations with positive cosmological constant is discussed and certain putative alternatives are shown to either solve different equations or to be the KSdS solution in disguise. A simultaneous no-hair and cosmic no-hair theorem for the KSdS geometry in the presence of an imperfect fluid is proved.