Abstract
Lun [1] one of the field equations may be interpreted as a generalisation of the \RT\ equation. Accordingly, by extensively investigating the \RT\ spacetimes [2] (whose evolutions are governed by the \RT\ equation) we are laying the groundwork for more general evolutions in the characteristic setting of Numerical Relativity.
We have devised numerical schemes which successfully evolve the \aRT\ equation using two distinct methods: finite differences and a spectral method (the latter proves superior). We are presently attempting to match a dust interior to the vacuum exterior. The first step in the matching is to determine the history of the collapsing surface by following eventually radial time-like geodesics backwards in retarded time from near the event horizon. We present preliminary results on the history of the shell of test particles. In general, as the test particles proceed backwards they acquire a tangential component to