From black hole spectral instability to stable observables

Abstract

The quasi-normal mode (QNM) spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this instability will be a technical challenge. Here we investigate the spectral instability of time-independent data. This leads us to study the Regge Poles (RP), the counterparts to the QNMs in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. Overall, the study proposes a novel and complementary approach on the black hole spectral instability phenomena which allows us to reveal a surprising and unexpected mechanism at play which protects scattering quantities from the instability.

5 + 3 pages, 4 + 2 figures, 1 table. Title changed. Matches the accepted version in Phys. Rev. Lett

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• Spectral instability of black holes: relating the frequency domain to the time domain
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Spectral instability of horizonless compact objects within astrophysical environments
• Natural polynomials for Kerr quasi-normal modes
• Exploring black holes with multiple photon spheres by interferometric signatures
• Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
• Dynamical system approach to the spectral (in)stability of black holes under localised potential perturbations