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arXiv · 2205.07470

Omniscient foliations and the geometry of cosmological spacetimes

Ivan P. Costa e Silva·Jose Luis Flores·Jonatan Herrera
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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.

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Ivan P. Costa e Silva, Jose Luis Flores, Jonatan Herrera. 2022-05-16. Omniscient foliations and the geometry of cosmological spacetimes. https://doi.org/10.1007/s10714-022-03033-z

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