Black holes in nonlinear electrodynamics: Quasinormal spectra and parity splitting

We discuss the quasinormal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasinormal 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 quasinormal 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-Nordstrom family and in this case it is well known that the quasinormal 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-Nordstrom black holes, and we show that in this case there is a parity splitting in the quasinormal mode spectra. A partial explanation for this phenomena is provided by considering the eikonal (high-frequency) limit.