Universal aspects of gravity localized on thick branes

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes, We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's law. We also comment on th possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scaler field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p + 2)-dimensions. (C) 2000 Elsevier Science B.V. All rights reserved.