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.

20 pages, 1 figure, minor revisions, final version

References in corpus (3)

• Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant
• Ultrarelativistic boost of the black ring
• On the completeness of impulsive gravitational wave space-times

Cited by in corpus (3)

• 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
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis