Spectrum instability and graybody factor stability for parabolic approximation of Regge-Wheeler potential
Phys. Rev. D 112, 024054 – Published 23 July, 2025
DOI: https://doi.org/10.1103/v3xt-r8nc
Abstract
We investigate the stability of quasinormal mode (QNM) spectra and graybody factors in the Schwarzschild black hole by approximating the Regge-Wheeler (R-W) potential with a piecewise parabolic form and treating the deviation as a perturbation. We find that QNM spectra are sensitive to small perturbations, while graybody factors remain stable. This piecewise parabolic approximated potential gives rise to the long-lived modes whose imaginary parts remain close to zero and decrease slowly with overtone number increasing. The reflection coefficient shows distinct resonance feature in the high-frequency regime that are absent in the original R-W case. For the calculation of graybody factors, we employ an analytic method based on transfer matrix technique, and this approach can also be effectively used in other effective potential cases.
