The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves

Abstract

We study geodesics in the complete family of expanding 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 rigorously prove existence and global uniqueness of continuously differentiable geodesics (in the sense of Filippov) and study their interaction with the impulsive wave. Thereby we justify the "$C^1$-matching procedure" used in the literature to derive their explicit form.

24 pages, 2 figures

References in corpus (5)

• Radiation from accelerated black holes in an anti-de Sitter universe
• Global hyperbolicity for spacetimes with continuous metrics
• Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• Photon rockets moving arbitrarily in any dimension

Cited by in corpus (14)

• Superboost transitions, refraction memory and super-Lorentz charge algebra
• The Poincaré and BMS flux-balance laws with application to binary systems
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Logarithmic Celestial Conformal Field Theory
• More on gravitational memory
• On geodesics in low regularity
• Gravitational and electromagnetic memory
• Penrose junction conditions extended: impulsive waves with gyratons
• 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
• Completeness of general pp-wave spacetimes and their impulsive limit
• Note on electromagnetic memories
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis
• Generalised hyperbolicity in spacetimes with Lipschitz regularity