On destabilising quasi-normal modes with a radially concentrated perturbation

TL;DR

This paper investigates how localized radial perturbations can destabilize black hole quasi-normal modes, analyzing different instability types, perturbation effects, and numerical methods to understand spectral instability.

Contribution

It introduces a specific model of a bump perturbation to study spectral instability of black hole quasi-normal modes and evaluates the effectiveness of pseudospectral numerical methods.

Findings

Identified two types of spectral instability in black hole modes.

Quantified the impact of perturbation size on destabilization.

Validated the pseudospectral method for this analysis.

Abstract

In this work we explore some aspects of the spectral instability of back hole quasi-normal modes, using a specific model as an example. The model is that of a small bump perturbation to the effective potential of linear axial gravitational waves on a Schwarzschild background, and our focus is on three different aspects of the instability: identifying and distinguishing between the two different types of instabilities studied previously in the literature, quantifying the size of the perturbations applied to the system and testing the validity of the pseudospectral numerical method in providing a convergent result for this measure, and finally, relating the size and other features of the perturbation to the degree of destabilisation of the spectrum.