Telling tails and quasi-resonances in the vicinity of Dymnikova regular black hole

TL;DR

This work analyzes the dynamics of a minimally coupled massive scalar field in the Dymnikova regular black-hole spacetime, focusing on quasinormal modes, late-time tails, and grey-body factors. It combines time-domain evolution with Prony analysis and a high-order WKB–Padé approach to map the spectrum across the mass parameter $μ$ and multipole index $ℓ$, revealing quasi-resonances and oscillatory late-time tails with a universal envelope $t^{-7/8}$. The study finds that increasing $μ$ raises the real part of the frequencies while decreasing the damping rate, and that grey-body factors are strongly suppressed for larger $μ$, signaling distinctive signatures of regular black holes. Overall, the results suggest that massive fields can probe near-horizon quantum corrections in the Dymnikova geometry and motivate further exploration of higher overtones, polar perturbations, and rotating or higher-dimensional generalizations.

Abstract

We investigate quasinormal modes, late-time tails, and grey-body factors for massive scalar perturbations in the background of the Dymnikova regular black hole. By applying both the time-domain integration and the WKB method with Padé improvements, we show that the spectrum of massive fields differs qualitatively from the massless case. The oscillation frequency of the dominant mode grows with the field mass $μ$, while the damping rate decreases, suggesting the existence of quasi-resonances at sufficiently large $μ$. In the time domain, the late-time signal exhibits oscillatory tails with a power-law envelope, whose decay rate matches analytic expectations. Grey-body factors are also computed, showing strong suppression of radiation when mass is increased. Taken together, these results indicate that massive fields provide distinctive signatures of regular black holes and may serve as probes of near-horizon quantum corrections in the Dymnikova geometry.

Figures (6)

• Figure 1: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=0$, $\mu=0.1$ (blue), $\mu=0.3$ (red), $\mu=0.6$ (green); $l_{cr}=1.137$.
• Figure 2: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=1$, $\mu=0.1$ (blue), $\mu=0.3$ (red), $\mu=0.6$ (green); $l_{cr}=1.137$.
• Figure 3: Effective potential and lograrithmic time-domain profile together with the line $\sim t^{-7/8}$ for $\ell=0$, $\mu=10$, $l_{cr}=1.137$, $M=1$.
• Figure 4: Effective potential and lograrithmic time-domain profile together with the line $\sim t^{-7/8}$ for $\ell=1$, $\mu=20$, $l_{cr}=1.137$, $M=1$.
• Figure 5: Effective potential and lograrithmic time-domain profile for $\ell=1$, $\mu=0.05$, $l_{cr}=1.137$, $M=1$. The quasinormal ringing period gives $\omega = 0.288725 - 0.0934358 i$, which is in a good agreement with the 12-th order WKB data $\omega = 0.287974 - 0.093852 i$, while the intermediate tail is close to the law $\sim t^{-5/2}$.