Compact Null Hypersurfaces and Collapsing Riemannian Manifolds

✍ Scribed by Alan D. Rendall

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 483 KB
• Volume: 193
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19981930110

✦ Synopsis

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 t o construct a family of three-dimensional Riemannian metrics which collapses with bounded curvature and applying known results on the topology of manifolds which collapse. T h e result is then applied t o general relativity, where it implies a restriction on the topology of smooth compact Cauchy horizons in spacetimes with various types of reasonable matter content.