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arXiv · 2404.06428

Maximality and Cauchy developments of Lorentzian length spaces

Olaf Müller
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Abstract

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.

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Olaf Müller. 2024-04-09. Maximality and Cauchy developments of Lorentzian length spaces. https://arxiv.org/abs/2404.06428

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