GeoTop Geometry Seminar: Eric Ling (KU@GeoTop)

Geometry Seminar (Geometric Analysis)

Speaker: Eric Ling (KU - GeoTop)

Title: Some results on topology and spacetime singularities

Abstract: There is an interesting connection between topology and spacetime singularities (i.e. null geodesic incompleteness). In the 70s, Gannon and Lee showed how one can use Penrose's singularity theorem to show that nontrivial topology in a spacetime leads to a singularity (assuming a mild asymptotically flat condition). In the presence of black hole horizons, Friedman et al. showed that the topology outside a black hole in an asymptotically flat spacetime must be trivial. These results were later expanded on by Galloway, Chruściel, Wald, Woolgar and others in different asymptotic settings. In this talk, I will discuss some recent results on topological censorship -- both in the asymptotically flat setting and the cosmological setting -- that don't rely on the existence of an explicit conformal null infinity. Time permitting, we will discuss some open questions about generating examples of such spacetimes.