Quasinormal frequencies of gravitational perturbation in regular black hole spacetimes

The quasinormal frequencies of gravitational perturbation around some well-known regular black holes were investigated in this work. We consider complete perturbations of the energy-momentum tensor of electromagnetic part for non-linear electrodynamics and gravitational field. By using the WKB approximation and the asymptotic iteration method, we make a detailed analysis of the gravitational QNM frequencies by varying the characteristic parameters of the gravitational perturbation and the spacetime charge parameters of the regular black holes. It is found that the imaginary part of quasinormal modes as a function of the charge parameter has different monotonic behaviors for different black hole spacetimes. Moreover, the asymptotic expressions of gravitational QNMs for l≫1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l \gg 1$$\end{document} are obtained by using the eikonal limit method. We demonstrate that the gravitational perturbation is stable in all these spacetimes.