  In [6], Geroch, Kronheimer and Penrose introduced a way to attach ideal
points to a spacetime M , defining the causal completion of M. They established
that this is a topological space which is Hausdorff when M is globally
hyperbolic. In this paper, we prove that if, in addition, M is simply-connected
and conformally flat, its causal completion is a topological manifold with
boundary homeomorphic to S x [0, 1] where S is a Cauchy hypersurface of M. We
also introduce three remarkable families of globally hyperbolic conformally
flat spacetimes and provide a description of their causal completions.
