Gravitational quasinormal modes of Dymnikova black holes

TL;DR

This work analyzes how quantum corrections encoded by a running gravitational coupling in the Dymnikova regular black hole affect gravitational quasinormal modes, focusing on axial perturbations. The dominant frequencies are computed via a WKB–Padé approach and validated by time-domain evolution, across varying $l_{ m cr}$. The results show that both the real part and the damping rate of the QNMs decrease with increasing $l_{ m cr}$, with the spectrum smoothly approaching Schwarzschild as $l_{ m cr}$ grows, and high-$6ell$ modes following the eikonal null-geodesic correspondence. The findings suggest that horizon-local quantum corrections imprint observable signatures in gravitational-wave ringdown, offering a potential test of Asymptotically Safe gravity and regular black-hole scenarios with future high-precision detectors.

Abstract

We investigate gravitational quasinormal modes of the Dymnikova black hole, a regular spacetime in which the central singularity is replaced by a de Sitter core. This geometry, originally proposed as a phenomenological model, also arises naturally in the framework of Asymptotically Safe gravity, where quantum corrections lead to a scale-dependent modification of the Schwarzschild solution. Focusing on axial gravitational perturbations, we compute the dominant quasinormal frequencies using the WKB method with Padé approximants and verify the results with time-domain integration. We find that the introduction of the quantum parameter $l_{\rm cr}$ leads to systematic deviations from the Schwarzschild spectrum: the real oscillation frequency decreases as $l_{\rm cr}$ increases, while the damping rate also becomes smaller, implying longer-lived modes. In the limit of large $l_{\rm cr}$, the quasinormal spectrum smoothly approaches the Schwarzschild case. These results suggest that even though the corrections are localized near the horizon, they leave imprints in the gravitational-wave ringdown which may become accessible to observation with future high-precision detectors.

Figures (4)

• Figure 1: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=2$, $l_{cr}=0.1$ (blue), $l_{cr}=1$ (red), $l_{cr}=1.137$ (green).
• Figure 2: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=3$, $l_{cr}=0.1$ (blue), $l_{cr}=1$ (red), $l_{cr}=1.137$ (green).
• Figure 3: Time-domain profile for $\ell=2$, $l_{cr}=1.137$. The Prony method gives $\omega = 0.369372 - 0.0856535 i$ for the fundamental mode $n=0$.
• Figure 4: Time-domain profile for $\ell=3$, $l_{cr}=1.137$. The Prony method gives $\omega = 0.59618 - 0.091002 i$ for the fundamental mode $n=0$.