Nonexpanding impulsive gravitational waves with an arbitrary cosmological constant

TL;DR

This paper constructs exact solutions for nonexpanding impulsive gravitational waves in backgrounds with any cosmological constant, unifying cases of de Sitter, anti-de Sitter, and Minkowski spaces using a 'cut and paste' method.

Contribution

It introduces a unified approach to derive explicit impulsive wave solutions in various cosmological backgrounds, including continuous and distributional metric forms.

Findings

Solutions are valid for de Sitter, anti-de Sitter, and Minkowski backgrounds.

Metrics are conformal to impulsive pp-waves, with explicit $ o 0$ limit.

The approach covers both continuous and distributional metric representations.

Abstract

Exact solutions for nonexpanding impulsive waves in a background with nonzero cosmological constant are constructed using a `cut and paste' method. These solutions are presented using a unified approach which covers the cases of de Sitter, anti-de Sitter and Minkowski backgrounds. The metrics are presented in continuous and distributional forms, both of which are conformal to the corresponding metrics for impulsive pp-waves, and for which the limit as $\Lambda\to 0$ can be made explicitly.