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The regularity of geodesics in impulsive pp-waves

  • Alexander Lecke
  • Roland Steinbauer
  • Robert Švarc
Research Article

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.

Keywords

Impulsive pp-waves Geodesics Carathéodory-solutions 

Mathematics Subject Classification (2010)

83C15 34A36 83C35 

Notes

Acknowledgments

We thank Jiří Podolský for kindly sharing his expertise and Clemens Sämann, and Milena Stojković for helpful discussions. This work was supported by FWF-grant P25326 and OeAD WTZ-project CZ15/2013 resp. 7AMB13AT003.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexander Lecke
    • 1
  • Roland Steinbauer
    • 1
  • Robert Švarc
    • 2
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Institute of Theoretical Physics, Faculty of Mathematics and PhysicsCharles University in PraguePraha 8Czech Republic

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