Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II

Abstract

We investigate all geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional metric. We extend the regularization approach of part I, [SSLP16] to a full nonlinear distributional analysis within the geometric theory of generalized functions. We prove global existence and uniqueness of geodesics that cross the impulsive wave and hence geodesic completeness in full generality for this class of low regularity spacetimes. This, in particular, prepares the ground for a mathematically rigorous account on the 'physical equivalence' of the continuous with the distributional `from' of the metric.

21 pages, 1 figure; v2: close to final version

References in corpus (6)

• The Penrose singularity theorem in regularity $C^{1,1}$
• The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• On the completeness of impulsive gravitational wave space-times
• Completeness of general pp-wave spacetimes and their impulsive limit
• Ordinary differential equations in algebras of generalized functions

Cited by in corpus (5)

• 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
• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis