Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics

TL;DR

This paper derives the quasinormal modes of nonlinear electromagnetic black holes using unstable null geodesics, providing insights into their oscillation spectra and comparing them with linear counterparts.

Contribution

It presents a method to calculate QNMs of nonlinear electromagnetic black holes via unstable null geodesics, extending previous linear analyses.

Findings

QNMs are determined by unstable null geodesics in the effective metric.

Calculated QNMs for four nonlinear black holes, including Euler-Heisenberg, Born-Infeld, and regular Bardeen black holes.

Comparison shows differences between nonlinear and linear electromagnetic black hole QNMs.

Abstract

The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for singular, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparison is shown with the QNMs of the linear electromagnetic counterpart, their Reissner-Nordstr\"{o}m black hole.