Asymptotic quasinormal modes, echoes, and black hole spectral instability: a brief review

TL;DR

This review discusses recent analytical advances in understanding black hole spectral instability, focusing on how small potential deformations affect quasinormal modes and the implications for gravitational wave observations and black hole echoes.

Contribution

It summarizes recent progress in analyzing black hole spectral instability, including the effects on quasinormal modes and potential observational signatures in gravitational wave data.

Findings

Low-lying modes are influenced by potential deformations.

High overtones relate to black hole echoes.

Spectral instability may produce observable signatures.

Abstract

We present a short review of the analytical aspects of recent progress in the study of black hole spectral instability and its potential observational consequences. This topic, inspired by earlier foundational works, has attracted considerable attention in the recent literature. It has been demonstrated that both the low-lying modes and high overtones of black hole quasinormal spectra can be substantially influenced by small deformations in the effective potential of the wave equation that describes black hole perturbations. The temporal evolution of gravitational wave signals is primarily governed by the first few low-lying quasinormal modes. In contrast, the asymptotic behavior of high overtones is closely associated with the phenomenon of black hole echoes. We review relevant studies on spectral instability in both regimes, highlighting their potential to produce substantial observational signatures in gravitational wave data. Additionally, recent proposals of Regge poles and reflectionless modes as alternative stable observables for probing black hole spacetimes are summarized.