Stability of generalized Einstein-Maxwell-scalar black holes

A bstract We study the stability of static black holes in generalized Einstein-Maxwell-scalar theories. derive master equations for odd and even parity perturbations. The sufficient necessary conditions under odd-parity perturbations are derived. show that these usually not similar to energy simplest case a minimally coupled scalar field. obtain even-parity also derived speed propagation five degrees freedom obtained class theories which all propagate at light. Finally, we have applied our results various nonlinear electrodynamics, scalar-tensor Einstein-Maxwell-dilaton theory. For latter, calculated quasinormal modes.