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A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves

Michael Kunzinger·Roland Steinbauer
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Abstract

The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions $(θ\de$, $θ^2\de$, $\de^2$). A solution concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is presented. Using a universal regularization procedure we prove existence and uniqueness results and calculate the distributional limits of these solutions explicitly. The obtained limits are regularization independent and display the physically expected behavior.

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Michael Kunzinger, Roland Steinbauer. 1999-04-19. A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves. https://doi.org/10.1063/1.532816

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