COMPACT NULL HYPERSURFACES AND COLLAPSING RIEMANNIAN-MANIFOLDS

Restrictions are obtained on the topology of a compact divergence-free null hypersurface in a four-dimensional Lorentzian manifold whose Ric ci tensor is zero or satisfies some weaker conditions. This is done by showing that each null hypersurface of this type can be used to const ruct a family of three-dimensional Riemannian metrics which collapses with bounded curvature and applying known results on the topology of m anifolds which collapse. The result is then applied to general relativ ity, where it implies a restriction on the topology of smooth compact Cauchy horizons in spacetimes with various types of reasonable matter content.