Why greybody factors remain insensitive to metric perturbations despite the spectral instability of Regge poles
Abstract
We examine the stability of black hole observables in the ringdown regime through an analysis of Regge poles and greybody factors. Recent studies by Rosato et al. and Oshita et al. proposed greybody factorsas more robust descriptors of black hole spectra than quasinormal modes, whose spectral instability is highly sensitive to ultraviolet perturbations of the metric. Motivated by this perspective, we investigate how Regge poles, central to the analytic structure of the scattering matrix in the complex angular momentum plane, characterize scattering and absorption phenomena for black holes with metric discontinuities. We extend the matrix method implemented in hyperboloidal coordinates to compute Regge poles under such discontinuities and validate the results by comparing them with a modified continued fraction approach. Using the resulting Regge pole spectrum, we evaluate the associated scattering amplitudes and total absorption cross sections. Our findings demonstrate that the stability of these observables across frequencies can be traced to the low-lying modes, while spectral bifurcations at higher frequencies signal the onset of instability induced by distant ultraviolet perturbations. Nevertheless, under the WKB approximation, these high-frequency deformations are shown to have limited observable impact, supporting the robustness of greybody factors as reliable signatures of black hole dynamics.
