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We study geodesics in the complete family of nonexpanding impulsivegravitational waves propagating in spaces of constant curvature, that isMinkowski, de Sitter and anti-de Sitter universes. Employing the continuousform of the metric we prove existence and uniqueness of continuouslydifferentiable geodesics (in the sense of Filippov) and use a C^1-matchingprocedure to explicitly derive their form.

The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves