Structure and stability of the Lukash plane-wave spacetime

TL;DR

This paper analyzes the stability of Lukash plane-wave spacetimes, revealing that their linear stability depends on the level of background shear anisotropy and identifying conditions for perturbation growth.

Contribution

It provides a covariant framework for analyzing the stability of Lukash spacetimes and links stability to shear anisotropy levels.

Findings

Stability depends on background shear anisotropy.

Higher shear leads to increased linear instability.

Conditions for perturbation growth are identified.

Abstract

We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by the Lukash metric. Combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the vacuum solution depends crucially on the background shear anisotropy. The stronger the deviation from the Hubble expansion, the more likely the overall linear instability of the model. Our analysis addresses rotational, shear and Weyl curvature perturbations and identifies conditions sufficient for the linear growth of these distortions.