Birefringence and QuasiNormal Modes of the Einstein-Euler-Heisenberg Black Hole

In this contribution we study the birefringence and the quasinormal modes (QNM) in the eikonal approximation, of the Einstein-Euler-Heisenberg black hole (EEH-BH) . The EEH-BH is an exact solution of the Einstein equations coupled to the Euler-Heisenberg nonlinear electrodynamics. It is well known that in the presence of strong electromagnetic fields light rays modify their trajectories and do follow the null geodesics of an effective metric as a result of the nonlinear interaction between light and the intense magnetic or electric background. In the Euler-Heisenberg theory the phenomenon of birefringence arises and then exist two possible light trajectories for polarized light in the vicinity of the EEH-BH. On the other hand, using the correspondence between the parameters of the null unstable geodesics and the quasinormal modes in the eikonal approximation. We determine these QNM for both, the electric and the magnetic EEH-BH and compare them with its linear counterpart, the Reissner-Nordstr\"{o}m black hole, since there are two effective metrics, to each one corresponds one null geodesic that renders two possible QNM from the same compact object.