Homogeneous Plane-wave Spacetimes and their Stability

TL;DR

This paper analyzes the stability of spatially homogeneous plane-wave spacetimes in various dimensions, identifying conditions under which they remain stable or become unstable, and extends the analysis to the Milne universe.

Contribution

It provides a comprehensive stability analysis of plane-wave spacetimes in (4+1) dimensions and generalizes results to arbitrary dimensions, distinguishing between stable and unstable cases.

Findings

Non-exceptional plane waves are stable to vacuum and certain matter perturbations.

Exceptional plane waves exhibit instability.

Milne universe is stable if the strong energy condition holds.

Abstract

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and find there are two cases to consider; what we call non-exceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In the exceptional case we always find an instability. Also we consider the Milne universe in arbitrary dimensions and find it is also stable provided the strong energy condition is satisfied. This implies that there exists an open set of stable plane-wave solutions in arbitrary dimensions.