Long-lived quasinormal modes and overtones' behavior of the holonomy corrected black holes

TL;DR

This paper investigates the quasinormal modes and overtones of various fields around holonomy corrected black holes, revealing their dependence on near-horizon geometry and the existence of long-lived massive modes, with analytical formulas derived.

Contribution

It provides a detailed analysis of overtones and fundamental modes of scalar, electromagnetic, and Dirac fields, including new analytical eikonal formulas and their extensions beyond the eikonal approximation.

Findings

Overtones depend on near-horizon geometry.

Fundamental mode localized near potential barrier peak.

Massive fields have arbitrarily long-lived modes.

Abstract

Recently massless test scalar field perturbations of the holonomy corrected black holes [Z. Moreira et. al. Phys. Rev. D 107 (2023) 10, 104016] were studied in order to estimate quantum corrections to the quasinormal spectrum of a black hole. Here we study both the fundamental mode and overtones of scalar, electromagnetic and Dirac fields with the help of the Leaver method and higher order WKB formula with Pad\'e approximants. We observe that the overtones depend on the geometry near the event horizon, while the fundamental mode is localized near the peak of the potential barrier, what agrees with previous studies. We showed that unlike a massless field, the massive one possesses arbitrarily long lived modes. We also obtain the analytical eikonal formula for quasinormal modes and its extension beyond eikonal approximation as a series in powers of $1/\ell$, where $\ell$ is the multipole number.