The regularity of geodesics in impulsive pp-waves

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 Caratheodory) are actually continuously differentiable, thereby rigorously justifying the 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
• Caratheodory solutions