2024/04/09 by Olaf Müller, Müller, Olaf
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2404.06428
This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly causal Lorentzian manifolds to the corresponding category of Lorentzian spaces, and considers three problems in the context of maximal Cauchy developments of Lorentzian spaces: The first is to define pointed Gromov-Hausdorff metrics for spatially and temporally noncompact Lorentzian spaces, the second to present an explicit non-spacetime example of a maximal globally hyperbolic Lorentzian space, the third to define canonical representatives for Cauchy developments. A certain well-posedness property for geodesics plays a key role in each of the problems.