On destabilising quasi-normal modes with a radially concentrated perturbation

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.

12 pages, 3 figures, contribution to Frontiers in Physics special issue "Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach"; v2 includes minor changes to match published version

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Cited by in corpus (9)

• Hyperboloidal Approach to Quasinormal Modes
• Pseudospectrum of rotating analog black holes
• Perturbing the vortex: quasinormal and quasibound spectra of rotating acoustic geometries
• Probing the Unstable Spectrum of Schwarzschild-like Black Holes
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Pseudospectrum and time-domain analysis of the EFT corrected black holes
• Vortices without inflow: bound spectra in horizonless rotational analogs
• Spectral instability of horizonless compact objects within astrophysical environments
• Overdamped quasibound states inside a Schwarzschild black hole