Gravitational collapse and the cosmological constant - art. no. 124005

We consider here the effects of a nonvanishing cosmological term on the fin al fate of a spherical inhomogeneous collapsing dust cloud. It is shown tha t, depending on the nature of the initial data from which the collapse evol ves, and for a positive value of the cosmological constant, we can have a g lobally regular evolution where a bounce develops within the cloud. We char acterize precisely the initial data causing such a bounce in terms of the i nitial density and velocity profiles for the collapsing cloud. In the cases otherwise, the result of collapse is either the formation of a black hole or a naked singularity resulting as the end state of collapse. We also show here that a positive cosmological term can cover a part of the singularity spectrum which is visible in the corresponding dust collapse models for th e same initial data.