Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of non-twisting type N solutions

TL;DR

This paper classifies all non-twisting Petrov-type N vacuum solutions with a cosmological constant, detailing their geometric properties and subclasses, and sets the stage for interpreting them as gravitational waves in de Sitter or anti-de Sitter backgrounds.

Contribution

It provides a comprehensive classification and explicit metrics for non-twisting Petrov-type N solutions with cosmological constant, linking them to gravitational wave propagation.

Findings

Solutions belong to Kundt or Robinson-Trautman classes.

Invariant subclasses are explicitly characterized.

Geometrical properties and relations are analyzed.

Abstract

All non-twisting Petrov-type N solutions of vacuum Einstein field equations with cosmological constant Lambda are summarized. They are shown to belong either to the non-expanding Kundt class or to the expanding Robinson-Trautman class. Invariant subclasses of each class are defined and the corresponding metrics are given explicitly in suitable canonical coordinates. Relations between the subclasses and their geometrical properties are analyzed. In the subsequent paper these solutions are interpreted as exact gravitational waves propagating in de Sitter or anti-de Sitter spacetimes.