Bonanno-Reuter regular black hole: quasi-resonances, grey-body factors and absorption cross-sections of a massive scalar field

TL;DR

This work investigates how a quantum-corrected Bonanno–Reuter black hole in asymptotically safe gravity modulates the dynamics of a massive scalar field. It combines a high-order WKB–Padé approach with time-domain integration to compute quasinormal modes, study full time evolution, and evaluate grey-body factors and absorption cross-sections. Increasing the field mass $\mu$ suppresses damping and promotes quasi-resonances, while late-time tails acquire an oscillatory envelope $\propto t^{-7/8}\sin(\mu t+\varphi)$, signaling dispersive massive propagation. The grey-body factors diminish at low frequency as $\mu$ grows, shifting the emission spectrum to higher frequencies, and the total cross-section tends to the geometric-optics limit at high $\Omega$, highlighting observable imprints of RG-improved quantum gravity on black-hole perturbations.

Abstract

We study quasinormal modes of a massive scalar field in the background of the regular, quantum-corrected Bonanno-Reuter black hole, which arises from the renormalization group improvement of the Schwarzschild solution within the framework of asymptotically safe gravity. The analysis is performed in both the time and frequency domains. We find that increasing the mass of the field leads to a strong suppression of the damping rate, and extrapolation to larger masses indicates the emergence of arbitrarily long-lived oscillations, or quasi-resonances. In the time domain, the late-time decay follows an asymptotic behavior that differs from the power-law tails of the classical Schwarzschild case. Furthermore, we compute the grey-body factors and absorption cross-sections for the massive scalar field and show that the grey-body factors decrease as the field mass increases, effectively shifting the emitted radiation spectrum toward higher frequencies.

Figures (9)

• Figure 1: Effective potentials for $\ell=0$$\gamma=0.1$, $\mu=0.05$: $M=1.66$ (blue, top), $M=2$ (black,middle), $M=10$ (red,bottom).
• Figure 2: Effective potentials for $\ell=0$$\gamma=0.1$, $\mu=0.5$: $M=1.66$ (blue, top), $M=2$ (black,middle), $M=10$ (red,bottom).
• Figure 3: Real and imaginary part of the dominant ($n=0$) quasinormal modes of the $\ell=1$, $M=1$ gravitational perturbations for the Bonanno-Reuter black hole calculated by the 6th-order WKB formula with Padé resummation ($[\tilde{m}/\tilde{n}] = [3/3]$) as functions of $\mu$, $\gamma=0.01$ (blue), $\gamma=1$ (red), $\gamma=9/2$ (black).
• Figure 4: Real and imaginary part of the dominant ($n=0$) quasinormal modes of the $\ell=2$, $M=1$ gravitational perturbations for the Bonanno-Reuter black hole calculated by the 6th-order WKB formula with Padé resummation ($[\tilde{m}/\tilde{n}] = [3/3]$) as functions of $\mu$, $\gamma=0.01$ (blue), $\gamma=1$ (red), $\gamma=9/2$ (black).
• Figure 5: Semi-logarithmic time-domain profiles for $\ell=1$ perturbations (left) and $\ell=2$ ones (right). Here $M=1.66$, $\gamma=0.1$. For the left plot WKB gives $\omega=0.203056- 0.046915 i$, while the Prony method gives $\omega =0.20446 - 0.04648 i$ making the relative error less than one percent. For the right plot we have $\omega = 0.3376 - 0.0462 i$ by the Prony method and $\omega =0.3376 - 0.0461 i$ by the WKB method.