Can we distinguish black holes with electric and magnetic charges from quasinormal modes?

We compute the quasinormal modes of static and spherically symmetric black holes (BHs) with electric and magnetic charges. For the electrically charged case, the dynamics of perturbations separates into the odd- and even-parity sectors with two coupled differential equations in each sector. In the presence of both electric and magnetic charges, the differential equations of four dynamical degrees of freedom are coupled with each other between odd- and even-parity perturbations. Despite this notable modification, we show that, for a given total charge and mass, a BH with mixed electric and magnetic charges gives rise to the same quasinormal frequencies for fundamental modes. This includes the case in which two BHs have equal electric and magnetic charges for each of them. Thus, the gravitational-wave observations of quasinormal modes during the ringdown phase alone do not distinguish between electrically and magnetically charged BHs.