Quasinormal Ringing and Unruh-Verlinde Temperature of the Frolov Black Hole

In this study, we investigate electromagnetic and Dirac test field 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 Averaging. 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.

💡 Research Summary

This paper investigates the response of a charged regular (nonsingular) black hole—known as the Frolov black hole—to test‑field perturbations of the electromagnetic and massless Dirac types. The Frolov metric is given by
( ds^{2}= -f(r)dt^{2}+ \frac{dr^{2}}{f(r)}+r^{2}(d\theta^{2}+\sin^{2}\theta d\phi^{2}))
with
( f(r)=1-\frac{(2Mr-q^{2}),r^{2}}{r^{4}+(2Mr+q^{2})\alpha_{0}^{2}}.)
Here (M) is the black‑hole mass, (q) is an effective charge parameter (0 ≤ q ≤ 1), and (\alpha_{0}) is a length scale that encodes quantum‑gravity corrections; setting (\alpha_{0}=0) recovers the Reissner‑Nordström (RN) solution, while (q=0) yields the Hayward regular black hole. The parameter (\alpha_{0}) introduces an effective de Sitter core with cosmological constant (\Lambda=3/\alpha_{0}^{2}) and modifies the horizon structure.

The authors first derive the master wave equations for the two test fields. For the electromagnetic perturbation, after expanding the vector potential in vector spherical harmonics and imposing the test‑field approximation, the field reduces to a Schrödinger‑like equation
(\frac{d^{2}\Psi_{\rm EM}}{dr_{*}^{2}}+