Spectrum instability and greybody factor stability for parabolic approximation of Regge-Wheeler potential

TL;DR

This paper studies the stability of quasinormal mode spectra and greybody factors for Schwarzschild black holes by approximating the Regge-Wheeler potential with a piecewise parabolic form, revealing sensitivities and resonances.

Contribution

It introduces a novel piecewise parabolic approximation of the Regge-Wheeler potential and analyzes its impact on QNM spectra and greybody factors, including resonance features.

Findings

QNM spectra are sensitive to small perturbations.

Greybody factors remain stable under the approximation.

Resonance features appear in the reflection coefficient at high frequencies.

Abstract

We investigate the stability of QNM spectra and greybody factors in the Schwarzschild black hole by approximating the Regge-Wheeler potential with a piecewise parabolic form and treating the deviation as a perturbation. We find that QNM spectra are sensitive to small perturbations, while greybody 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 greybody factors, we employ an analytic method based on transfer matrix technique, and this approach can also be effectively used in other effective potential cases.