Abstract We study gravitational quasinormal modes of the Hayward spacetime, a regular black-hole geometry that also admits an interpretation as an effective quantum-corrected solution within asymptotically safe gravity. Using both the higher-order WKB method supplemented with Padé approximants and time-domain integration with Prony analysis, we obtain accurate spectra for axial perturbations and explore the impact of the quantum parameter γ. We find that increasing γ systematically raises the oscillation frequencies while reducing the damping rates, making the ringdown longer lived. For the first overtone, the effect of γ is noticeably stronger than for the fundamental mode, providing an indication of the so-called “outburst of overtones” previously observed for test fields, and pointing to the particular sensitivity of subdominant modes to near-horizon quantum corrections. In addition, the analytic approximation for quasinormal modes are obtained in the form of expansion beyond the eikonal limit.
Bolokhov et al. (Mon,) studied this question.