Topological restrictions in Lorentzian geometry: a survey

It is well know that globally hyperbolic solutions (M,g) of the Einstein field equations in general relativity may have initial data Cauchy hypersurfaces with any topology. However, some restrictions on the fundamental group of M can arise from the causal structure if either all inextendible causal geodesics in (M,g) are complete or if one assumes that M has a boundary with suitable properties. I shall review a number of such "topological censorship" results and discuss some open issues.Universidad de Málaga. Campus de excelencia Internacional Andalucía Tech

Omniscient foliations and the geometry of cosmological spacetimes

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.Comment: 19 pages, no figure