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Geodesics for impulsive gravitational waves and the multiplication of distributions

H. Balasin
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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 $θ(0)$. 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.

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H. Balasin. 1996-07-30. Geodesics for impulsive gravitational waves and the multiplication of distributions. https://doi.org/10.1088/0264-9381%2F14%2F2%2F018

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