Black holes in nonlinear electrodynamics: quasi-normal spectra and parity splitting

TL;DR

This paper investigates the quasi-normal modes of black holes influenced by nonlinear electrodynamics, revealing parity splitting in spectra for deformed Reissner-Nordström black holes, a phenomenon not present in the Maxwell case.

Contribution

First computation of coupled electromagnetic-gravitational quasi-normal frequencies for nonlinear electrodynamic black holes, highlighting parity splitting effects.

Findings

Parity splitting observed in quasi-normal spectra for nonlinear cases

Deformed Reissner-Nordström black holes exhibit distinct spectra

Eikonal limit provides partial explanation for parity phenomena

Abstract

We discuss the quasi-normal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasi-normal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasi-normal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, the unique spherically symmetric black hole solutions are described by the Reissner-Nordstr\"om family and in this case it is well-known that the quasi-normal spectra in the even- and odd-parity sectors are identical to each other. However, when moving away from the Maxwell case, we obtain deformed Reissner-Nordstr\"om black holes, and we show that in this case there is a parity splitting in the quasi-normal mode spectra. A partial explanation for this phenomena is provided by considering the eikonal (high-frequency) limit.