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 ₂ₑ leads to systematic deviations from the Schwarzschild spectrum: the real oscillation frequency decreases as l ₂ₑ increases, while the damping rate also becomes smaller, implying longer-lived modes. In the limit of large l ₂ₑ, 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.
Lütfüoğlu et al. (Mon,) studied this question.