The stability of the greybody factor of Hayward black hole

TL;DR

This paper examines the stability of the greybody factor of Hayward black holes under small potential perturbations, introducing new quantitative measures and analyzing their behavior with different methods.

Contribution

It introduces the $ ext{G}$-factor and $ ext{H}$-factor to quantify greybody factor stability and compares their behavior using equal amplitude and equal energy methods.

Findings

The $ ext{G}$-factor and $ ext{H}$-factor are bounded by the amplitude or energy of the bump.

Factors tend to specific values or zero depending on the method as the bump moves away from the horizon.

The greybody factor shows stability under certain perturbations, insensitive to the black hole's regular parameter.

Abstract

In this study, we investigate the stability of the greybody factor of Hayward black holes by adding a small bump to the effective potential. Since the greybody factor depends on frequency, we introduce the $\mathcal{G}$-factor and $\mathcal{H}$-factor to quantitatively characterize its stability. We study the stability of the greybody factor within the equal amplitude method and the equal energy method, respectively. Here, the equal amplitude method can be directly imposed by fixing the amplitude of the bump, while the equal energy method requires a physical definition of the energy of the bump with the assistance of hyperboloidal framework. For both methods, when the location of the bump is close to the event horizon of the black hole, and the closer it is to the peak of the original potential, the larger are $\mathcal{G}$-factor and $\mathcal{H}$-factor, and they are bounded by the magnitude of the amplitude or the energy. More importantly, for the equal amplitude method, two factors tend to a specific value as the location of the bump increases. In contrast, for the equal energy method, two factors converge to zero as the location of the bump increases. Notably, the $\mathcal{G}$-factor and the $\mathcal{H}$-factor are insensitive to the regular parameter of Hayward black hole. Therefore, our results indicate that the greybody factor is stable under specific perturbations.