(In)stability of the black hole greybody factors and ringdowns against a small-bump correction

TL;DR

This paper investigates the stability of black hole greybody factors against small perturbations, finding they are stable at ringdown frequencies but destabilized at higher frequencies, supporting their use in modeling ringdown amplitudes.

Contribution

It demonstrates the stability of greybody factors at relevant frequencies and clarifies their behavior under small-bump corrections using WKB analysis.

Findings

Greybody factors are stable at ringdown frequencies.

Destabilization occurs at higher frequencies with sharper bumps.

WKB analysis explains the (in)stability behavior.

Abstract

Recently, it has been proposed that the black hole greybody factors can be important to model ringdown spectral amplitudes. We study the stability of greybody factors against a small-bump correction in the perturbation equation. We find (I) that the greybody factor is stable in the frequency region relevant to ringdown and (II) that it is destabilized at higher frequencies, especially for a sharper bump correction. This behavior is similar to the case of higher overtones, which is also very sensitive to a small correction. We clarify this (in)stability with the WKB analysis. As the greybody factor is stable at the frequency region relevant to the main part of ringdown, we conclude that the greybody factor is suitable to model ringdown amplitude. In order to investigate a bump correction in a self-consistent manner, we consider the small-bump correction that can be realized in the general framework of effective field theory of black hole perturbations.