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

TL;DR

The study tests the robustness of the grey-body factor–quasinormal mode correspondence in a quantum-corrected regular black hole geometry by analyzing axial gravitational perturbations of the Hayward metric. It computes grey-body factors using a 6th-order WKB method and compares them to predictions based on the fundamental quasinormal mode $\omega_0$ and first overtone $\omega_1$ following the Konoplya 2024 scheme, incorporating corrections through $K$ and Padé resummation. Quantum corrections parameterized by $\gamma$ raise the near-horizon potential barrier, suppressing both the grey-body factors $\Gamma_{\ell}(\Omega)$ and the absorption cross-section $\sigma(\Omega)$, while the QNM–grey-body correspondence remains accurate to within a few percent for low multipoles and improves for higher $\ell$. These results support the universality of the QNM–grey-body link in quantum-corrected, regular spacetimes and motivate future work on polar perturbations, rotation, and more general quantum-corrected geometries.

Abstract

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 $γ$, 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.

Figures (5)

• Figure 1: Effective potentials for $\ell=2$ (left) and $\ell=3$ (right) axial gravitational perturbations: $M=1$, $\gamma=0.01$ (bottom), $\gamma=0.6$ (middle), and $\gamma=32/27$ (top).
• Figure 2: Grey-body factors of $\ell=2$ axial gravitational perturbations calculated by the 6th order WKB method and via the correspondence with QNMs: $M=1$, $\gamma=0.01$ (top, blue), $\gamma=0.6$ ( middle, red), and $\gamma=32/27$ (bottom, black).
• Figure 3: Grey-body factors of $\ell=3$ axial gravitational perturbations calculated by the 6th order WKB method and via the correspondence with QNMs: $M=1$, $\gamma=0.01$ (top, blue), $\gamma=0.6$ ( middle, red), and $\gamma=32/27$ (bottom, black).
• Figure 4: Grey-body factors of $\ell=4$ axial gravitational perturbations calculated by the 6th order WKB method and via the correspondence with QNMs: $M=1$, $\gamma=0.01$ (top, blue), $\gamma=0.6$ ( middle, red), and $\gamma=32/27$ (bottom, black).
• Figure 5: Absorption cross-section for gravitons for the first ten multipoles $\ell=2,3,...11$ together with the total cross-section (black curve)