Institute for Mathematical Physics a Rigorous Solution Concept for Geodesic and Geodesic Deviation Equations in Impulsive Gravitational Waves a Rigorous Solution Concept for Geodesic and Geodesic Deviation Equations in Impulsive Gravitational Waves

The geodesic as well as the geodesic deviation equation for impulsive gravi-tational waves involve highly singular products of distributions (, 2 , 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.