Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I

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.

32 pages, 3 figures, minor revisions, included "Part I" in the title, final version

References in corpus (3)

• Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant
• The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
• On the completeness of impulsive gravitational wave space-times

Cited by in corpus (8)

• The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
• Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
• Penrose junction conditions extended: impulsive waves with gyratons
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II
• Spacetime geometry fluctuations and geodesic deviation
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis