Symmetries and geodesics in (anti-)de Sitter spacetimes with nonexpanding impulsive waves

TL;DR

This paper analyzes exact solutions of nonexpanding impulsive waves in (anti-)de Sitter spacetimes, revealing their symmetries and geodesic behavior, and compares them to impulsive pp-waves in flat spacetime.

Contribution

It provides a unified geometrical framework to find symmetries and explicit geodesics in these spacetimes, extending understanding of impulsive gravitational waves with a cosmological constant.

Findings

Spacetimes admit at least three global Killing vectors.

Explicit geodesic solutions are derived.

Symmetries and geodesics reduce to known solutions when the cosmological constant vanishes.

Abstract

We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on test particles. Timelike geodesics in the axially-symmetric Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for vanishing cosmological constant, the symmetries and geodesics reduce to those for well-known impulsive pp-waves.