Stability criterion of 1+1 dilatonic black hole

We study the stability of the black hole that is a solution of the 2d dilaton gravity derived from string-theoretical models. We do this by means of the Quasinormal Modes (QNM) approach. In order to find the QNM of this geometry, we consider perturbations described by a massive scalar field non-minimally coupled to gravity. We find that the QNM frequencies turn out to be pure imaginary, consequently leading to purely damped modes, in agreement with the literature of dilatonic black holes. Our result exhibits a large range of stability for this geometry against the scalar perturbations that excite the overtone with n > μ, μ, being a dimesionless parameter related to the mass of the black hole. We consider both the minimal coupling case, i.e. for which the coupling parameter ζ vanishes, and the case ζ = 1/4 .