Regge poles, greybody factors, and absorption cross sections for black hole metrics with discontinuity

It was recently proposed by Rosato et al. and Oshita et al. that the black hole graybody factors, as stable observables at relatively high frequencies, are more relevant quantities than quasinormal modes in modeling ringdown spectral amplitudes. The proposed alternative was primarily motivated by the observed spectral instability of quasinormal modes, which was shown to be highly sensitive to ultraviolet metric perturbations. It was argued that the overall contributions of spectrally unstable quasinormal modes conspire to produce stable observables through collective interference effects. Regge poles, which govern the analytic structure of the S-matrix in the complex angular momentum plane, also serve as an effective tool for assessing the scattering processes of black holes. In this regard, the present study investigates the Regge poles and the total absorption cross sections for black hole metrics with discontinuity. Specifically, these quantities are evaluated at given frequencies and scattering angles, which account for the contributions of the graybody factors at different angular momenta. To this end, we generalize the matrix method to evaluate the Regge poles in black hole metrics with discontinuity. To ascertain our approach, the numerical results are compared with those obtained using a modified version of the continued fraction method. The obtained Regge pole spectrum is then used to calculate the scattering amplitude and cross section. We show that the stability of these observables as functions of the frequency can be readily interpreted in terms of the stability of the Regge pole spectrum, particularly the low-lying modes. Nonetheless, destabilization still occurs at larger frequencies, characterized by the emergence of a bifurcation in the spectrum. The latter further evolves, leading to more significant deformation in the Regge poles, triggered by ultraviolet metric perturbations moving farther away from the black hole. However, based on the validity of the WKB approximation, it is argued that such an instability in the spectrum is not expected to cause significant observable implications.