Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions $n\geq 4$

TL;DR

This paper proves the global existence and stability of de Sitter-like solutions in higher-dimensional Einstein-Yang-Mills systems, extending previous four-dimensional results to all spacetime dimensions n ≥ 4.

Contribution

It generalizes Friedrich's stability results from four dimensions to all higher spacetime dimensions n ≥ 4 for Einstein-Yang-Mills equations.

Findings

Established global future stability of de Sitter-like solutions in n ≥ 4 dimensions.

Extended stability results from 4D to higher dimensions.

Demonstrated robustness of solutions under non-linear perturbations.

Abstract

We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in $n \geq 4$ spacetime dimension. This generalizes Friedrich's Einstein-Yang-Mills stability results in dimension $n=4$ [ J Differ Geom 34 (1991), 275-345] to all higher dimensions.