Anna Sakovich: Towards a spacetime intrinsic flat convergence

I will present our joint work with Christina Sormani aimed at rigorously defining the notion of spacetime intrinsic flat convergence, a low regularity notion of convergence in the Lorentzian setting. As a first step, a spacetime needs to be converted into a metric space using the cosmological time function of Andersson, Galloway and Howard and the null distance of Sormani and Vega. Together with Christina Sormani, we have shown that the causal structure of these spaces can be recovered from the null distance and the cosmological time. We can also prove that a distance-preserving time-preserving bijection between the spacetimes endowed with a null distance is in fact a Lorentzian isometry under suitable conditions. Furthermore, for 'nice' spacetimes there are also biLipschitz charts so that we may view the spacetimes endowed with the null distance as integral current spaces. This, in particular, can be used to rigorously define the spacetime intrinsic flat convergence for certain classes of spacetimes.