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.