Omniscient foliations and the geometry of cosmological spacetimes

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