Looking at the Gregory-Laflamme instability through quasi-normal modes

TL;DR

This paper investigates the Gregory-Laflamme instability of black strings by analyzing quasinormal modes and time-domain profiles, revealing how parameters like wave vector and extra dimensions influence stability and mode behavior.

Contribution

It provides numerical analysis of quasinormal modes and time evolution of black string perturbations, highlighting the threshold behavior and mode crossing phenomena.

Findings

Identification of quasinormal modes in stable and unstable regimes

Observation of tiny oscillations near the stability threshold

Evidence of mode crossing affecting time domain profiles

Abstract

We study evolution of gravitational perturbations of black strings. It is well known that for all wavenumber less than some threshold value, the black string is unstable against scalar type of gravitational perturbations, which is named the Gregory-Laflamme instability. Using numerical methods, we find the quasinormal modes and time-domain profiles of the black string perturbations in the stable sector and also show the appearance of the Gregory-Laflamme instability in the time domain. The dependence of the black string quasinormal spectrum and late time tails on such parameters as the wave vector and the number of extra dimensions is discussed. There is a numerical evidence that in the threshold point of instability the static solution of the wave equation is dominant. For wavenumbers slightly larger than the threshold value, in the region of stability, we see tiny oscillations with very small damping rate. While, for wavenumbers slightly smaller than the threshold value, in the region of the Gregory-Laflamme instability, we observe tiny oscillations with very small growth rate. We also find the level crossing of imaginary part of quasinormal modes between the fundamental mode and the first overtone mode, which accounts for the peculiar time domain profiles.