The regularity of geodesics in impulsive pp-waves |
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| Authors: | Alexander Lecke Roland Steinbauer Robert Švarc |
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| Affiliation: | 1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090?, Vienna, Austria
2. Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V?Hole?ovi?kách?2, 180?00?, Praha 8, Czech Republic
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| Abstract: | We consider the geodesic equation in impulsive pp-wave space-times in Rosen form, where the metric is of Lipschitz regularity. We prove that the geodesics (in the sense of Carathéodory) are actually continuously differentiable, thereby rigorously justifying the ${mathcal C}^1$ -matching procedure which has been used in the literature to explicitly derive the geodesics in space-times of this form. |
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