Asymptotically AdS Solutions of Five Dimensional Gravity-Dilaton Theory

Abstract

We search for Asymptotically AdS solutions of the background metric in which dilaton back reacts to gravity in five-dimensional gravity-dilaton theory. The five-dimensional gravity-dilaton theory generally appears in the context of the low energy effective action of closed string theory in the Einstein frame. In particular, we consider dilaton which are minimally coupled to gravity in which the potential for dilation is taken to be simple and contain only one exponential term parametrized by a constant a. We solve analytically and show for a simple constant dilaton potential it appears there are no black hole solutions if we turn on the dilaton contribution. On the other hand, the exponential dilaton potential has black hole solutions but they are not in general Asymptotically AdS. We argue that there are some possible Asymptotically AdS black hole solutions in the range of