Quasinormal modes and stability criterion of dilatonic black holes 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 under 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 nonminimally coupled to gravity. We find that the QNMs frequencies turn out to be pure imaginary leading to purely damped modes, in the range 0 <zeta < 1/4 of nonminimal coupling constant (zeta), and the QNMs acquires a real part if zeta > 1/4 that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of the considered geometry against scalar perturbations. We study the instability for different values of nonminimal coupling constant. We extend our results to the 4+1 dimensional dilatonic black hole, where the metric is the product of a two-dimensional asymptotically flat geometry and a three-sphere with constant radius, which are completely decoupled from each other. The exact solution for the QNMs was obtained in the five-dimensional case.