Properties of the Null Distance and Spacetime Convergence

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of spacetime, gives rise to an intrinsic, conformally invariant metric that induces manifold topology. We show when warped products low regularity globally hyperbolic spacetimes endowed with are (local) integral current spaces. This structure sets stage investigating convergence analogous Riemannian geometry. Our main theorem is a general result product relating uniform, Gromov--Hausdorff Sormani--Wenger intrinsic flat corresponding distances. In addition, we non-uniform warping functions in leads distinct limiting behavior, such as limits disagree.