Quasinormal Modes and Stability Criterion of Dilatonic Black Hole in 1+1 and 4+1 Dimensions

We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions against to scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order to find the QNMs corresponding to a black hole geometry, we consider perturbations described by a massive scalar field non-minimally coupled to gravity. We find that the QNM's frequencies turn out to be pure imaginary leading to purely damped modes, that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of the considered geometry against the scalar perturbations. We consider both the minimal coupling case, i.e., for which the coupling parameter $\zeta$ vanishes, and the case $\zeta={1/4}$.