Perturbations of generic Kasner spacetimes and their stability

TL;DR

This paper studies the stability of generic Kasner spacetimes under linear perturbations, revealing divergence of Weyl tensor perturbations at early and late times except in specific cases, highlighting stability conditions.

Contribution

It provides a detailed analysis of the stability of Kasner spacetimes, identifying conditions under which perturbations remain bounded or diverge.

Findings

Weyl tensor perturbations diverge at late times in most Kasner spacetimes.

At early times, divergence occurs unless specific conditions on perturbations are imposed.

The Kasner spacetime as a product of Milne and Euclidean spaces remains stable under perturbations.

Abstract

This article investigates the stability of a generic Kasner spacetime to linear perturbations, both at late and early times. It demonstrates that the perturbation of the Weyl tensor diverges at late time in all cases but in the particular one in which the Kasner spacetime is the product of a two-dimensional Milne spacetime and a two-dimensional Euclidean space. At early times, the perturbation of the Weyl tensor also diverges unless one imposes a condition on the perturbations so as to avoid the most divergent modes to be excited.