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 Bonanno et al. (Phys Rev Lett 132:031401, https://doi.org/10.1103/PhysRevLett.132.031401 , arXiv:2308.10890 [gr-qc], 2024). 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 by comparing the WKB grey-body factors with accurate QNM frequencies, finding excellent agreement, especially for larger multipole numbers $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> .