Linear stability of the Linet - Tian solution with negative cosmological constant

TL;DR

This paper investigates the linear stability of the Linet - Tian spacetime with negative cosmological constant, finding it to be unstable under gravitational perturbations due to boundary condition issues at infinity.

Contribution

It extends the analysis of Levi-Civita metric stability to include negative cosmological constant, revealing inherent instabilities in the Linet - Tian solutions.

Findings

Unstable modes are present under a broad set of boundary conditions.

Negative cosmological constant alters the structure at infinity, affecting stability analysis.

Linet - Tian spacetimes with negative cosmological constant are linearly unstable.

Abstract

In this paper we analyze the linear stability of the Linet - Tian solution with negative cosmological constant. In the limit of vanishing cosmological constant the Linet - Tian metric reduces to a form of the Levi - Civita metric, and, therefore, it can be considered as a generalization of the former to include a cosmological constant. The gravitational instability of the Levi - Civita metric was recently established, and the purpose of this paper is to investigate what changes result from the introduction of a cosmological constant. A fundamental difference brought about by a (negative) cosmological constant is in the structure at infinity. This introduces an added problem in attempting to define an evolution for the perturbations because the constant time hypersurfaces are not Cauchy surfaces. In this paper we show that under a large set of boundary conditions that lead to a unique evolution of the perturbations, we always find unstable modes, that would generically be present in the evolution of arbitrary initial data, leading to the conclusion that the Linet - Tian space times with negative cosmological constant are linearly unstable under gravitational perturbations.