Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

TL;DR

This paper derives explicit refraction formulas for geodesics crossing impulsive gravitational waves in constant-curvature spacetimes, providing a detailed geometric analysis of test particle motion in these exact solutions.

Contribution

It introduces continuous metric forms and explicit junction conditions for geodesics in impulsive gravitational wave spacetimes with cosmological constant.

Findings

Derived simple refraction formulas for all geodesic types

Provided a detailed geometric description in axially symmetric cases

Analyzed motion in spacetimes with snapped cosmic strings

Abstract

We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in Minkowski, de Sitter or anti-de Sitter universe. Using the continuous form of these metrics we derive explicit junction conditions and simple refraction formulae for null, timelike and spacelike geodesics crossing a general impulse of this type. In particular, we present a detailed geometrical description of the motion of test particles in a special class of axially symmetric spacetimes in which the impulse is generated by a snapped cosmic string.