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.