  In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology $R^3$ with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology $S^2$. These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.
