  We present preliminary results in our long-term project of studying the
evolution of matter in a dynamical spacetime. To achieve this, we have
developed a new code to evolve axisymmetric initial data sets corresponding to
a black hole surrounded by matter fields. The code is based on the coupling of
two previously existing codes. The matter fields are evolved with a 2D
shock-capturing method which uses the characteristic information of the GR
hydro equations to build up a linearized Riemann solver. The spacetime is
evolved with a 2D ADM code designed to evolve a wormhole in full general
relativity. An example of the kind of problems we are currently investigating
is the on axis collision of a star with a black hole.
