  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
the 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 scalar field cannot produce conformally-flat locally intersecting brane
configurations or a p-brane in greater than (p+2)-dimensions.

High Energy Physics - Theory;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology