R. A. Konoplya

We study quasinormal modes of scalar, electromagnetic, and Dirac perturbations of four-dimensional regular black holes arising in non-polynomial quasi-topological gravity. Starting from a more general class of metric functions constructed within the same framework, from which two representative cases are selected for detailed analysis, we examine their spectral properties. While the fundamental mode changes smoothly with the regularization parameter, higher overtones display a markedly enhanced sensitivity to near-horizon modifications, leading to the characteristic outburst of overtones. Remarkably, pushing the WKB approximation to sufficiently high orders with Pade resummation already allows one to detect the onset of this effect. Time-domain analysis and the Leaver method confirm that the relative error of the higher-order WKB approach is much smaller than the observed effect. Our results indicate that overtone dynamics provides a sensitive probe of geometrically regular black holes and that high-order WKB methods remain capable of capturing nontrivial spectral features beyond the fundamental mode.