Proper-Time Approach in Asymptotic Safety via Black Hole Quasinormal Modes and Grey-body Factors

TL;DR

This work investigates how near-horizon quantum corrections in an asymptotically safe gravity background modify black-hole quasinormal modes and grey-body factors by analyzing massless test fields (scalar, electromagnetic, Dirac) on a quantum-corrected metric with deformation parameter $q$. The authors compute fundamental QNMs using a 6th-order WKB method with Padé resummation and time-domain integration, and they supplement these with a WKB-based computation of grey-body factors and a QNM–grey-body correspondence. They find that deviations from Schwarzschild are strongest in the near-extremal regime ($q$ near $q_{ ext{cr}}$), mainly affecting the damping rates, while the late-time tails remain Schwarzschild-like; the grey-body factors exhibit detectable suppression, though the QNM–grey-body correspondence holds to within a few percent. The results demonstrate that ringdown and Hawking spectra remain sensitive probes of near-horizon quantum modifications and provide robust tools for testing asymptotically safe gravity scenarios.

Abstract

We study the quasinormal mode spectrum and grey-body factors of black holes in an effectively quantum-corrected spacetime, focusing on the influence of near-horizon modifications on observable quantities. Employing scalar, electromagnetic, and Dirac test fields, we analyze the perturbation equations and extract the fundamental quasinormal frequencies using both the 6th-order WKB method with Padé resummation and time-domain integration. Our results show that quantum corrections near the horizon significantly affect the real and imaginary parts of the quasinormal modes, particularly for low multipole numbers and in the near-extremal regime. We also verify the robustness of the correspondence between quasinormal modes and grey-body factors by comparing WKB results with those reconstructed from the dominant quasinormal modes. Across all field types and parameter ranges considered, the WKB method proves accurate within a few percent, confirming its reliability in probing the impact of near-horizon physics. These findings support the use of quasinormal ringing and Hawking radiation spectra as sensitive tools for testing quantum modifications of black hole spacetimes.

Figures (11)

• Figure 1: Effective potential for a scalar (left), electromagnetic (middle) and Dirac (right) perturbations for $q=20$ (black), $q=2$ (red) and $q=1.38$ (blue). The potentials are positive definite outside the external event horizon.
• Figure 2: Real part of the fundamental QNMs ($n=0$) for scalar perturbations $s=0$ for $\ell=0$ (left), $\ell=1$ (middle) and $\ell =2$ (right).
• Figure 3: Real part of the fundamental QNMs ($n=0$) for electromagnetic perturbations $s=1$ for $\ell=1$ (left), $\ell=2$ (middle) and $\ell =3$ (right).
• Figure 4: Real part of the fundamental QNMs ($n=0$) for Dirac perturbations $s=1/2$ for $\ell=1/2$ (left), $\ell=3/2$ (middle) and $\ell =5/2$ (right).
• Figure 5: Imaginary part of the fundamental QNMs ($n=0$) $s=0$ (left), $s=1$, and $s=1/2$. Red is for the lowest multipole $\ell=s$, blue is for $\ell=s+1$ and black is $\ell=s+2$.