Geodesics for impulsive gravitational waves and the multiplication of distributions

Abstract

We consider particle trajectories in the gravitational field of an impulsive pp-wave. Due to the distributional character of the wave profile one inevitably encounters an ambiguous point value $\theta (0)$. We show that this ambiguity may be resolved by imposing covariant constancy of the square of the tangent. Our result is consistent with Colombeau's multiplication of distributions.

14 pages, latex2e, amstex macros, no figures

References in corpus (3)

• The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor
• Boosting the Kerr-geometry into an arbitrary direction
• Symmetries of pp-Waves with Distributional Profile

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