Abstract:

Topological censorship is a basic principle of spacetime physics. It is a set of results that establishes the topological simplicity at the fundamental group level of the domain of outer communications (the region outside all black holes and white holes) under a variety of physically natural circumstances. An important precursor to the principle of topological censorship, which serves to motivate it, is the Gannon-Lee singularity theorem. All of these results are spacetime results, i.e., they involve conditions that are essentially global in time. From the evolutionary point of view, there is the difficult question of determining whether a given initial data set will give rise to a spacetime satisfying these conditions. In order to separate out the principle of topological censorship from these difficult questions of global evolution, it would be useful to have a pure initial data version of topological censorship. In this talk we give a brief review of topological censorship, and we formulate and present such an initial data version for 3-dimensional initial data sets. The approach taken here relies on recent developments in the existence theory for marginally outer trapped surfaces, and leads to a nontime-symmetric version of the purely Riemannian results of Meeks-Simon-Yau. Geometrization plays an essential role in the proofs. Results in higher dimensions will also be discussed. This talk is based on joint work with Michael Eichmair and Dan Pollack.