Stability of BTZ black strings

TL;DR

This paper investigates the stability of BTZ black strings under fermonic and gravitational perturbations, revealing threshold-dependent stability that aligns with thermodynamic predictions, indicating the black string phase is not always the most stable configuration.

Contribution

It provides a detailed analysis of the stability thresholds for BTZ black strings against various perturbations, connecting dynamical stability with thermodynamic considerations.

Findings

Existence of threshold values for perturbation stability.

Stability depends on the mass squared parameter m^2.

Thermodynamic predictions align with dynamical stability results.

Abstract

We study the dynamical stability of the BTZ black string against fermonic and gravitational perturbations. The BTZ black string is not always stable against these perturbations. There exist threshold values for $m^2$ related to the compactification of the extra dimension for fermonic perturbation, scalar part of the gravitational perturbation and the tensor perturbation, respectively. Above the threshold values, perturbations are stable; while below these thresholds, perturbations can be unstable. We find that this non-trivial stability behavior qualitatively agrees with that predicted by a thermodynamical argument, showing that the BTZ black string phase is not the privileged stable phase.