Scalar charge of black holes in Einstein-Maxwell-dilaton theory

Abstract: We show that the monopole scalar charge of black holes in Einstein--Maxwell--dilaton theory is proportional to the electric potential at the event horizon, with a proportionality factor given by (minus) the scalar coupling constant. We also show that the scalar charge, in the weak electric charge limit, does not depend on the black hole spin. This result can be very useful to circumvent spin degeneracy issues when testing the theory against gravitational waves observations.