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

TL;DR

This paper proves the existence, uniqueness, and C^1-regularity of geodesics in a broad class of nonexpanding impulsive gravitational waves across various constant curvature spacetimes, using a continuous metric approach.

Contribution

It establishes the C^1-regularity and explicit form of geodesics in impulsive gravitational waves in Minkowski, de Sitter, and anti-de Sitter spaces, extending previous results.

Findings

Existence and uniqueness of geodesics proven

Explicit C^1-form of geodesics derived

Applicable to multiple constant curvature backgrounds

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.