Sensitivity of black hole spectral instability against perturbations of the effective potential

TL;DR

This paper investigates the surprising sensitivity of black hole spectral instability, especially the fundamental quasinormal mode, to small perturbations in the effective potential, revealing diverse instability phenomena.

Contribution

It provides analytical and numerical examples demonstrating the strong sensitivity and diversity of black hole spectral instability caused by effective potential perturbations.

Findings

Fundamental modes are highly sensitive to small potential perturbations.

The nature of perturbations depends on the potential shape and perturbation location.

Different perturbation types lead to qualitatively distinct instability behaviors.

Abstract

Black hole spectral instability is counterintuitive and contradicts many plausible assumptions of the properties of black hole quasinormal modes. The present study aims to explore different types of instability phenomena. It is understood that the fundamental mode is surprisingly sensitive to small perturbations of the effective potential of the linearized wave equation. Such perturbations can be produced by small-scale modifications of the spacetime metrics. From both the analytical and numerical perspectives, we elaborate on a few qualitatively different examples illustrating the strong sensitivity and diversity in black hole spectral instability caused by such effective potential perturbations. It turns out that the qualitative way in which the fundamental mode becomes perturbed depends on many factors such as the shape of the potential and how the perturbation changes as it moves away from the central black hole.