Gravitational perturbations of Dymnikova black holes: grey-body factors and absorption cross-sections

We study axial gravitational perturbations of the Dymnikova regular black hole, an asymptotically flat spacetime in which the Schwarzschild singularity is replaced by a de Sitter core. Using the WKB method with Padé approximants, we compute grey-body factors, and absorption cross-sections, and test the recently proposed correspondence between quasinormal frequencies and transmission coefficients. We find that variations of the quantum parameter \(lcr\) affect the effective potential only near the horizon, leading to minor deviations of grey-body factors and absorption cross-sections from the Schwarzschild case. As a result, the Hawking radiation spectrum is governed mainly by the modified Hawking temperature, with grey-body factors providing only subleading corrections. Unlike higher quasinormal overtones, which are highly sensitive to near-horizon deformations, the grey-body factors remain robust, a feature explicitly confirmed for the Dymnikova geometry. The correspondence between quasinormal modes and grey-body factors holds in our case with high accuracy for multipoles ≥ 2.