Exact Solutions in 5-D Brane Models With Scalar Fields

In this talk we consider the problem of a scalar field, non-minimally coupled to gravity through a -ξφ2Rterm, in the presence of a Brane. A number of exact solutions, for a wide range of values of the coupling parameter φ for both A-dependent and A-independent Brane tension, are presented. The behavior and general features of these solutions are discussed. We derive solutions for the scalar field compatible with the Randall-Sundrum metric and also geometries which can accomodate a folded kink-like scalar. Analytic and numerical results are provided for the case of a Brane or for smooth geometries, where the scalar field acts as a thick Brane. We also discuss briefly the graviton localization in our setup and demonstrate the characteristic volcano-like localizing potential for gravitons