Null Hypersurfaces in de Sitter and anti-de Sitter Cosmologies

TL;DR

This paper explores the geometry of null hypersurfaces in de Sitter and anti-de Sitter spacetimes, focusing on gravitational waves with a cosmological constant, and presents detailed examples related to impulsive waves and plane-fronted waves.

Contribution

It introduces new forms of de Sitter and anti-de Sitter line elements based on null hypersurfaces, extending the understanding of gravitational waves in these cosmological backgrounds.

Findings

Derived specific null hypersurface geometries in constant curvature spacetimes

Analyzed impulsive gravitational wave collisions with cosmological constant

Generalized plane-fronted gravitational waves to include cosmological constant

Abstract

The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in space-times of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision space-time is a solution of Einstein's field equations with a cosmological constant, and the second originated in the generalisation of plane fronted gravitational waves with parallel rays to include a cosmological constant.