Monday 13 January 2020, 15:30-16:30 in HG03.085
Annegret Burtscher (RU)
On the metric structure and convergence of spacetimes
One of the most powerful objects in geometry are curves. Minimizing the arc lengths of curves between two points on Riemannian manifolds defines a distance function which induces a natural length metric space structure on the manifold. In turn, notions of metric convergence interact with the Riemannian structure and (weak) curvature bounds. No such profound metric theory is yet available for Lorentzian manifolds because the Lorentzian distance function does not give rise to a metric. For spacetimes with suitable time functions, however, the recently introduced null distance of Sormani and Vega provides an alternative metric that naturally interacts with the causal structure and also yields a length metric space and an integral current space. In this talk we compare the metric space structure of Riemannian and Lorentzian manifolds and show how different notions of metric convergence interact with the null distance of warped product spacetimes. This is joint work with Brian Allen.