Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity

Abstract

In this paper, we present a detailed study of axial gravitational perturbations of the regular black hole solution in asymptotically safe gravity, as proposed in \cite{Bonanno:2023rzk}. We analyze the quasinormal mode (QNM) spectrum of this black hole using two numerical techniques: the Bernstein spectral method and the asymptotic iteration method (AIM). These approaches allow us to compute QNM frequencies with high accuracy, even for higher overtones. Our results show that the fundamental mode is only weakly affected by the deviation parameter, whereas notable deviations from the Schwarzschild case emerge for higher overtones. Additionally, we examine the correspondence between grey-body factors and QNMs using the sixth-order WKB approximation, finding excellent agreement, especially for larger multipole numbers l.

Figures (7)

• Figure 1: The metric function $f(r)$ for various $\xi$.
• Figure 2: The effective potential $V (r_{*})$ of the axial gravitational perturbations as a function of the tortoise coordinate for different $l$ with $\xi$ = 0.2 (left panel) and for different $\xi$ with $l = 2$ (right panel).
• Figure 3: Complex frequencies of the fundamental $n=0, \ell=2$ mode as a function of the parameter $\xi$.
• Figure 4: $\text{Re}(\omega)$ (left panel) and $\text{Im}(\omega)$ (right panel) as functions of $\xi$ for the fundamental mode and first six overtones (top to bottom) with $\ell=2$.
• Figure 5: $\text{Re}(\omega)$ (left panel) and $\text{Im}(\omega)$ (right panel) as functions of $\xi$ for the fundamental mode and first nine overtones (top to bottom) with $\ell=3$.