Some regularity results for Lorentz-Finsler spaces

Abstract

We prove that for continuous Lorentz-Finsler spaces timelike completeness implies inextendibility. Furthermore, we prove that under suitable locally Lipschitz conditions on the Finsler fundamental function the continuous causal curves that are locally length maximizing (geodesics) have definite causal character, either lightlike almost everywhere or timelike almost everywhere. These results generalize previous theorems by Galloway, Ling and Sbierski, and by Graf and Ling.

arXiv comment18 pages, 3 figures. v2: added two figures

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• A Lorentzian analog for Hausdorff dimension and measure
• Aspects of $C^0$ causal theory
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• Uniqueness and non-uniqueness results for spacetime extensions
• On the asymptotic assumptions for Milne-like spacetimes
• Low regularity extensions beyond Cauchy horizons
• Uniqueness of maximal spacetime boundaries