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

Abstract

We study geodesics in the complete family of nonexpanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter universes. Employing the continuous form of the metric we prove existence and uniqueness of continuously differentiable geodesics (in the sense of Filippov) and use a C^1-matching procedure to explicitly derive their form.

arXiv comment20 pages, 1 figure, minor revisions, final version

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• Global hyperbolicity for spacetimes with continuous metrics
• Sturm-Liouville and Carroll: at the heart of the Memory Effect
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Ion Traps and the Memory Effect for Periodic Gravitational Waves
• Lorentz meets Lipschitz
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
• Penrose junction conditions extended: impulsive waves with gyratons
• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II
• Generalised hyperbolicity in spacetimes with Lipschitz regularity
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis