Abstract. We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a general regularisation technique we prove existence and uniqueness of geodesics crossing the wave impulse leading to a completeness result. We also derive the explicit form of the geodesics thereby confirming previous results derived in a heuristic approach.

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 Carathéodory) 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.

We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler-Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi's theorem on conjugate points and Noether's theorem. We close with an application to low regularity Riemannian geometry.

Abstract. Gelfand-Shilov spaces of the type S α α (R d ) and α α (R d ) can be realized as sequence spaces by means of the Hermite representation Theorem. In this article we show that for a function, where 1 2 ≤ α ≤ β (resp.

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