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Compact null hypersurfaces and collapsing Riemannian manifolds

Alan D. Rendall
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Abstract

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

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Alan D. Rendall. 1995-10-06. Compact null hypersurfaces and collapsing Riemannian manifolds. https://arxiv.org/abs/dg-ga/9510002

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