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arXiv · 2009.08834

Lorentz meets Lipschitz

Christian Lange·Alexander Lytchak·Clemens Sämann
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Abstract

We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $\mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\alpha$-H\"older continuous Lorentzian metric admit a $\mathcal{C}^{1,\frac{\alpha}{4}}$-parametrization.

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BibTeXRIS

Christian Lange, Alexander Lytchak, Clemens Sämann. 2020-09-18. Lorentz meets Lipschitz. https://doi.org/10.4310/atmp.2021.v25.n8.a4

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