Gregory Galloway

University of Miami, September 5, 12:30 pm

Topology and singularities in cosmological spacetimes

A theme in general relativity of long standing interest (at least to the speaker!) concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness). Many such results center around the notion of topological censorship, which has to do with black hole formation and the topology of black holes. In this talk we focus on the cosmological setting. More specifically, for 3+1 dimensional spacetimes which are spatially closed (i.e. whose spatial sections are compact without boundary), we establish a precise connection between the topology of these spatial slices and the occurrence of past singularities. This result applies to spacetimes with positive cosmological constant, where, for example, Hawking’s cosmological singularity theorem in general does not. Instead we will make use of Penrose’s singularity theorem (for which Penrose was awarded half the Nobel Prize in Physics in 2020). The proof also makes use of fundamental existence results for minimal surfaces and results in 3-manifold topology that were motivated by Thurston’s geometrization conjecture. We will begin the talk with some basic background in spacetime geometry. This is joint work with Eric Ling.