Exact impulsive gravitational waves in spacetimes of constant curvature

TL;DR

This paper reviews exact impulsive gravitational wave solutions in constant curvature spacetimes, detailing methods of construction and specific solutions like null multipole particles and snapping strings, with analysis of their properties.

Contribution

It provides a unified review of methods to construct impulsive gravitational waves in Minkowski, de Sitter, and anti-de Sitter spaces, including new solutions involving null multipole particles and colliding strings.

Findings

Descriptions of nonexpanding impulsive waves from null multipole particles.

Analysis of expanding spherical impulses from snapping and colliding strings.

Summary of geodesics and properties of impulsive wave spacetimes.

Abstract

Exact solutions exist which describe impulsive gravitational waves propagating in Minkowski, de Sitter, or anti-de Sitter universes. These may be either nonexpanding or expanding. Both cases in each background are reviewed here from a unified point of view. All the main methods for their construction are described systematically: the Penrose "cut and paste" method, explicit construction of continuous coordinates, distributional limits of sandwich waves, embedding from higher dimensions, and boosts of sources or limits of infinite accelerations. Attention is concentrated on the most interesting specific solutions. In particular, the nonexpanding impulsive waves that are generated by null multipole particles are described. These generalize the well-known Aichelburg-Sexl and Hotta-Tanaka monopole solutions. Also described are the expanding spherical impulses that are generated by snapping and colliding strings. Geodesics and some other properties of impulsive wave spacetimes are also summarized.