Probing the Unstable Spectrum of Schwarzschild-like Black Holes

TL;DR

This paper examines the stability of quasinormal modes in Schwarzschild-like black holes using pseudospectrum analysis, revealing inherent instabilities contrary to some recent claims about potential stabilization through random perturbations.

Contribution

It demonstrates that physically motivated deformations of Schwarzschild-like black holes lead to unstable quasinormal spectra, challenging previous ideas about stabilization via random potential perturbations.

Findings

Schwarzschild-like black holes exhibit unstable quasinormal spectra.

Pseudospectra lack features of stable wave operators.

Adding ad-hoc deformations confirms instability.

Abstract

We investigate the pseudospectrum of a Schwarzschild-like spacetime within the framework of black hole perturbation theory to analyze a counterintuitive assertion regarding the instability of quasinormal modes. Recent findings suggest that random perturbations to the effective potential associated with gravitational waves may enhance the stability of the underlying wave operator, thereby yielding a stable spectrum of randomly displaced quasinormal modes. Given the unphysical nature of such random perturbations, this work examines these findings within a spacetime that inherently exhibits a perturbed quasinormal spectrum. We find that, in contrast to the QNM spectrum of the Schwarzschild spacetime under random perturbations, the quasinormal spectrum of a Schwarzschild-like black hole deformed through a physically motivated implementation of the Rezzolla-Zhidenko parametrization is unstable. In particular, we show that the pseudospectra of these Schwarzschild-like black holes do not display the typical features associated with wave operators that yield stable quasinormal spectra. We corroborate our findings by computing the quasinormal spectra when additional (ad-hoc) deformations are added to the effective potential of the Rezzolla-Zhidenko black hole. We also argue that when multiple perturbation sources are present, identifying the origin of the instability may be difficult.