On the stability of homogeneous black strings in AdS

TL;DR

This paper investigates the stability of homogeneous black strings in Anti-de Sitter space, analyzing both generic and fine-tuned non-generic perturbations, revealing potential instability modes under specific conditions.

Contribution

It extends previous stability analyses by identifying a non-generic perturbation that could cause instability, requiring the scalar field to be absent during evolution.

Findings

Linear stability under generic perturbations confirmed.

Existence of a fine-tuned non-generic unstable mode.

Scalar field absence is crucial for the instability to manifest.

Abstract

In this paper we extend the analysis of the stability of an homogeneous black string in the presence of a negative cosmological constant with minimally coupled scalar fields. We recall the linear stability of this solutions under generic perturbations on the metric and of the scalar fields. Then, we extend the study of the stability by presenting the existence of a non-generic perturbation which may lead to an unstable behavior. The later mode is fine-tuned since it requires the scalar field degree of freedom to be absent through the whole evolution of the system.