  In the context of the Randall-Sundrum (RS) single-brane scenario, we discuss
the bulk geometry and dynamics of a cosmological brane in terms of the local
energy conservation law which exists for the bulk that allows slicing with a
maximally symmetric 3-space. This conservation law enables us to define a local
mass in the bulk. We show that there is a unique generalization of the dark
radiation on the brane, which is given by the local mass. We find there also
exists a conserved current associated with the Weyl tensor, and the
corresponding local charge, which we call the Weyl charge, is given by the sum
of the local mass and a certain linear combination of the components of the
bulk energy-momentum tensor. This expression of the Weyl charge relates the
local mass with the projected Weyl tensor, $E_{\mu\nu}$, which plays a central
role in the geometrical formalism of the RS braneworld. On the brane, in
particular, this gives a decomposition of the projected Weyl tensor into the
local mass and the bulk energy-momentum tensor. Then, as an application of
these results, we consider a null dust model for the bulk energy-momentum
tensor and discuss the black hole formation in the bulk. We investigate the
causal structure by identifying the locus of the apparent horizon and clarify
possible brane trajectories in the bulk. We find that the brane stays always
outside the black hole as long as it is expanding. We also find an upper bound
on the value of the Hubble parameter in terms of the matter energy density on
the brane, irrespective of the energy flux emitted from the brane.
