Quasinormal Modes and Gray-Body Factors for Gravitational Perturbations in Asymptotically Safe Gravity

TL;DR

This work analyzes axial gravitational perturbations of a fully regular black hole in Asymptotically Safe Gravity (the BMP geometry), focusing on quasinormal modes (QNMs) and gray-body factors. Quantum corrections are modeled via an effective anisotropic fluid, leading to a master equation with potential $V(r)$ and a tortoise coordinate $r_*$; QNMs and gray-body factors are computed using higher-order JWKB with Padé refinements and time-domain integration, with cross-checks from Prony fits. The main findings are that quantum corrections increase the oscillation quality factor (damping is reduced) and suppress gray-body factors, while late-time tails follow the universal Price law $|\Psi|\sim t^{-(2\ell+3)}$ independent of $\xi$, and the eikonal QNM–geodesic correspondence remains valid. The results have potential implications for Planck-scale black holes and primordial black hole evaporation, and the study validates the QNM–gray-body relation in this quantum-corrected setting, suggesting avenues for extending the analysis to higher overtones with Leaver’s method.

Abstract

A quantum-corrected black hole model arising from gravitational collapse in the framework of Asymptotically Safe Gravity was recently proposed in [A. Bonanno, D. Malafarina, A. Panassiti, Phys. Rev. Lett. 132, 031401 (2024)]. Quantum correction becomes considerable for Planck-scale black holes and strongly deviates from the Schwarzschild solution near the event horizon, quickly merging with the Schwarzschild metric in the far region. While quasinormal modes and gray-body factors have been analyzed for test fields in this background, no such analysis has yet been performed for gravitational perturbations. In this work, we study axial gravitational perturbations of these black holes by modeling the effective quantum corrections through an anisotropic fluid energy-momentum tensor. We compute both quasinormal modes and gray-body factors, and show that quantum corrections enhance the quality factor of the oscillations, thereby making the quantum-corrected black hole a more efficient gravitational wave emitter. At asymptotically late times, the power-law decay is indistinguishable from Price's tails, which behave as \( \sim t^{-(2\ell + 3)} \), where \( \ell \) is the multipole number. We also demonstrate that quantum corrections lead to a suppression of the gray-body factors and examine the validity of the correspondence between gray-body factors and quasinormal modes.

Figures (6)

• Figure 1: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=2$, $\xi=0.01$ (blue), $\xi=0.2$ (red), $\xi=0.45$ (green).
• Figure 2: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=3$, $\xi=0.01$ (blue), $\xi=0.2$ (red), $\xi=0.45$ (green).
• Figure 3: Left panel: Semi-logarithmic time-domain profile for $\ell=2$, $\xi=0.45$, $M=1$. The fundamental mode given by the Prony method is $\omega = 0.40033 - 0.07234 i$, which is in excellent concordance with the JWKB result $\omega = 0.400330 - 0.072338 i$. Right panel: The asymptotic tail (logarithmic scale) for the same values of the parameters together with the line $|\Psi| = A \cdot t^{-7}$, where $A$ is a constant.
• Figure 4: Left panel: Semi-logarithmic time-domain profile for $\ell=2$, $\xi=0.455$, $M=1$. The fundamental mode given by the Prony method is $\omega = 0.400669 - 0.0720145 i$, which is in excellent concordance with the JWKB result $\omega = 0.400668 - 0.072007 i$. Right panel: The asymptotic tail (logarithmic scale) for the same values of the parameters together with the line $|\Psi| = A \cdot t^{-7}$, where $A$ is a constant.
• Figure 5: Left panel: Gray-body factors obtained by the 6th order JWKB approach and via the correspondence with QNMs $\ell=2$, $\xi=0.01$ (blue) and $\xi=0.45$ (red); $M=1$. Right panel: Difference between gray-body factors from both methods.