Quasinormal modes of four-dimensional regular black holes in quasi-topological gravity: Overtones' outburst via WKB method

TL;DR

This paper investigates the quasinormal modes of various perturbations in four-dimensional regular black holes within quasi-topological gravity, revealing that higher overtones are highly sensitive to near-horizon modifications and can be effectively analyzed using high-order WKB methods.

Contribution

It demonstrates that high-order WKB methods with Pade resummation can detect overtone outbursts in regular black holes, providing a new way to probe their near-horizon geometry.

Findings

Higher overtones show enhanced sensitivity to near-horizon changes.

High-order WKB with Pade resummation accurately captures overtone behavior.

Overtone dynamics serve as a sensitive probe of regular black hole geometries.

Abstract

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.