Gravitational perturbations of the Hayward spacetime and testing the correspondence between quasinormal modes and grey-body factors

The paper studies axial gravitational perturbations of the Hayward black hole, a regular geometry that also arises as an effective solution in asymptotically safe gravity. By computing grey-body factors with the 6th-order WKB method and comparing them to predictions based on the quasinormal modes, the correspondence between transmission coefficients and quasinormal spectra is verified. Quantum corrections, parametrized by $\gamma$, are shown to suppress both the grey-body factors and the absorption cross-section, while the correspondence remains accurate at the percent level for low multipoles and essentially exact for higher ones.