# Annegret Burtscher: Spacetime convergence for warped products

**Time: **
Thu 2019-11-14 11.00 - 12.00

**Lecturer: **
Annegret Burtscher, Radboud University

**Location: ** Seminar Hall Kuskvillan, Institut Mittag-Leffler

### Abstract

Riemannian manifolds naturally carry the structure of metric spaces, and standard notions of metric convergence interact with the Riemannian structure and (weak) curvature bounds. Since the Lorentzian distance does not give rise to a metric structure, it is not obvious how to extend this theory to Lorentzian manifolds and generalizations thereof. For spacetimes with suitable time functions, the null distance of Sormani and Vega can be defined and is a metric that naturally interacts with the causal structure and yields an integral current space. Based on these results we compare different notions of convergence for the null distance of warped product spacetimes, in particular, we show that uniform, Gromov-Hausdorff and Sormani-Wenger intrinsic flat convergence agree if the sequence of (continuous) warping functions converges uniformly. This is joint work with Brian Allen.