Quasinormal ringing and Unruh-Verlinde temperature of the Frolov Black Hole

TL;DR

The study analyzes axial perturbations of the charged regular Frolov black hole by deriving master wave equations for massless electromagnetic and Dirac fields and computing their quasinormal mode (QNM) frequencies and grey-body factors using high-order WKB with Padé averaging. It also evaluates the Unruh-Verlinde temperature to quantify how quantum-gravity corrections modify near-horizon thermodynamics. The results show that increasing the charge parameter $q$ or the regularization scale $\alpha_{0}$ raises $\mathrm{Re}(\omega)$ and reduces damping $|\mathrm{Im}(\omega)|$, while low-frequency transmission is suppressed and the Unruh temperature is lowered. These findings indicate distinct observational signatures of regular black holes in ringdown and Hawking emission, linking quantum gravity corrections to measurable quantities. The work lays groundwork for future studies of gravitational perturbations and Hawking spectra in quantum-corrected spacetimes.

Abstract

In this study, we investigate electromagnetic and Dirac field axial-perturbations of a charged regular black hole arising from quantum gravity effects, commonly referred to as the Frolov black hole, a regular (nonsingular) black hole solution. We derive the master wave equations for massless electromagnetic and Dirac perturbations and solve them using the standard Wentzel-Kramers-Brillouin (WKB) method along with Padé approximation. From these solutions, we extract the dominant and overtone quasinormal mode (QNM) frequencies along with the associated grey-body factors, highlighting the deviations introduced by quantum gravity corrections compared to the classical case of Reissner-Nordström black hole. Furthermore, we analyze the Unruh-Verlinde temperature of this spacetime, providing quantitative estimates of how quantum gravity effects influence both quasinormal ringing and particle emission in nonsingular black hole models.

Figures (11)

• Figure 1: The metric function $f(r)$ as a funtion of $r$ for various values of $\alpha_0$ and with a fixed $q =0$ Increasing $\alpha_0$ shifts the curve upward and modifies the horizon structure.
• Figure 2: The metric function $f(r)$ as a funtion of $r$ for various values of $\alpha_0$ and with a fixed $q =0.5$ Increasing $\alpha_0$ shifts the curve upward and modifies the horizon structure.
• Figure 3: The metric function $f(r)$ as a funtion of $r$ for various values of $\alpha_0$ and with a fixed $q = 1$ Increasing $\alpha_0$ shifts the curve upward and modifies the horizon structure.
• Figure 4: The variation of $V(r)$ with the tortoise coordinate $r_\ast$ for varying values of $\alpha_0$ = 0 (red), 0.2 (blue), 0.4 (green), 0.76 (purple) taking $q=0.2$, $l = 2$, $M=1$ for the massless electromagnetic perturbations.
• Figure 5: The variation of $V(r)$ with the tortoise coordinate $r_\ast$ for different values of $q$ = 0 (red), 0.3 (blue), 0.6 (green) with fixed angular momentum number $l = 2$, and $\alpha_0 = 0.2$ for the massless electromagnetic perturbations, taking $M = 1$.