Lorentz meets Lipschitz (Q2674218)

This paper is devoted to the study of maximal causal curves for a Lipschitz continuous Lorentzian metric. The authors prove that these causal curves admit a \(\mathcal{C}^{1,1}\)-parametrization and, in such parametrization, they solve the geodesic equation in the sense of Filippov. The proof shows that maximal causal curves are either everywhere light-like or everywhere time-like. Furthermore, it demonstrates that maximal causal curves for an \(\alpha\)-Hölder continuous Lorentzian metric admit a \(\mathcal{C}^{1,\frac{\alpha}{4}}\)-parametrization.