Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes

Abstract

Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling and the black hole charge. We also show that while gravitational modes are only weakly affected by the coupling with the dilaton, the spectrum of electromagnetic modes exhibits a more pronounced dilaton-dependent breaking of isospectrality between the axial and polar sectors. We further show that the gravitational quasinormal modes are well approximated by the properties of unstable null circular geodesics in those spacetimes, while the treatment of electromagnetic and scalar modes can be simplified by a suitably modified Dudley-Finley scheme for the perturbed equations.