# Gravitational quasinormal modes of the Hayward spacetime

## TL;DR

This paper investigates how quantum corrections in the Hayward spacetime influence gravitational quasinormal modes, revealing that quantum parameters significantly affect oscillation frequencies and damping, with implications for black hole ringdown signals.

## Contribution

It provides the first detailed analysis of gravitational quasinormal modes in the Hayward spacetime, incorporating quantum corrections and advanced computational methods.

## Key findings

- Increasing quantum parameter $\gamma$ raises oscillation frequencies.
- Higher $\gamma$ reduces damping rates, prolonging ringdown.
- Overtones are more sensitive to quantum effects than fundamental modes.

## 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 Pade approximants and time-domain integration with Prony analysis, we obtain accurate spectra for axial perturbations and explore the impact of the quantum parameter $\gamma$. We find that increasing $\gamma$ systematically raises the oscillation frequencies while reducing the damping rates, making the ringdown longer lived. For the first overtone, the effect of $\gamma$ 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.