  In the Randall-Sundrum scenario we investigate the dynamics of a spherically
symmetric 3-brane world when matter fields are present in the bulk. To analyze
the 5-dimensional Einstein equations we employ a global conformal
transformation whose factor characterizes the $Z_2$ symmetric warp. We find a
new set of exact dynamical collapse solutions which localize gravity in the
vicinity of the brane for a stress-energy tensor of conformal weight -4 and a
warp factor that depends only on the coordinate of the fifth dimension.
Geometries which describe the dynamics of inhomogeneous dust and generalized
dark radiation on the brane are shown to belong to this set. The conditions for
singular or globally regular behavior and the static marginally bound limits
are discussed for these examples. Also explicitly demonstrated is complete
consistency with the effective point of view of a 4-dimensional observer who is
confined to the brane and makes the same assumptions about the bulk degrees of
freedom.
