  In the Randall-Sundrum scenario we analize the dynamics of a spherically
symmetric 3-brane when matter fields propagate in the bulk. For a well defined
class of conformal fields of weight -4 we determine a new set of exact
5-dimensional solutions which localize gravity in the vicinity of the brane and
are stable under radion field perturbations. Geometries which describe the
dynamics of inhomogeneous dust, generalized dark radiation and homogeneous
polytropic dark energy are shown to belong to this set.
