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

TL;DR

This paper analyzes gravitational perturbations of quantum-corrected black holes in Asymptotically Safe Gravity, revealing enhanced oscillation quality factors and suppressed gray-body factors, with implications for gravitational wave emission and black hole decay.

Contribution

It provides the first analysis of axial gravitational perturbations, quasinormal modes, and gray-body factors for quantum-corrected black holes in this framework, incorporating effective anisotropic fluid modeling.

Findings

Quantum corrections increase the quality factor of gravitational oscillations.

Gray-body factors are suppressed due to quantum effects.

Late-time decay follows Price's tail behavior, unaffected by quantum corrections.

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.