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.

final version, minor changes, reference added

References in corpus (1)

• Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

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