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 with the Euler-Heisenberg nonlinear electrodynamics. In the Euler-Heisenberg theory the phenomenon of birefringence arises and then there exists two possible light trajectories in the vicinity of the EEH-BH. On the other hand, using the correspondence between the parameters of the unstable null geodesics and the QNM in the eikonal approximation we have determined the QNM of gravitational and electromagnetic perturbations for both the electric and the magnetic EEH-BH and we compared them with their linear counterpart, the Reissner-Nordstr\"om black hole. Regarding electromagnetic perturbations we have to consider that there are two effective optical metrics and to each one corresponds one null geodesic that renders two electromagnetic QNMs from the same compact object.

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