Omniscient foliations and the geometry of cosmological spacetimes

Abstract

We identify certain general geometric conditions on a foliation of a spacetime (M,g) by timelike curves that will impede the existence of null geodesic lines, especially if (M,g) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on the geometry of cosmological spacetimes, in the context of Bartnik's splitting conjecture. Since the (non)existence of null lines is actually a conformally invariant property, such conditions only need to apply for some suitable conformal rescaling of g.

arXiv comment19 pages, no figures

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Cited by in corpus (2)

• Minimal Elements of the Causal Boundary with Applications to Spacetime Splitting
• Remarks on causal decrease, omniscient foliations and null lines in spacetimes