VACUUM SPACETIMES WITH FUTURE TRAPPED SURFACES

We show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data are defined o n a manifold with topology R(3) With a regular centre and are asymptot ically flat. Furthermore, these initial data will contain a shell-like region which is foliated by two-surfaces of topology S-2. These two-s urfaces are future trapped in the language of Penrose. The Penrose sin gularity theorem guarantees that the vacuum spacetime which evolves fr om this initial data is future null incomplete.