Impulsive waves in the Nariai universe

TL;DR

This paper introduces new exact solutions describing impulsive waves in the Nariai universe, analyzing their properties, special subclasses, and generalizations to related backgrounds, connecting to known impulsive wave solutions.

Contribution

It presents a novel class of impulsive wave solutions in the Nariai universe using a six-dimensional embedding formalism, including special subclasses and generalizations.

Findings

Impulsive waves propagate in the Nariai universe with non-expanding spherical wave fronts.

Special subclasses include pure gravitational waves and shells of null dust.

Solutions connect to known impulsive pp-waves when the cosmological constant and electromagnetic field vanish.

Abstract

A new class of exact solutions is presented which describes impulsive waves propagating in the Nariai universe. It is constructed using a six-dimensional embedding formalism adapted to the background. Due to the topology of the latter, the wave front consists of two non-expanding spheres. Special sub-classes representing pure gravitational waves (generated by null particles with an arbitrary multipole structure) or shells of null dust are analyzed in detail. Smooth isometries of the metrics are briefly discussed. Furthermore, it is shown that the considered solutions are impulsive members of a more general family of radiative Kundt spacetimes of type-II. A straightforward generalization to impulsive waves in the anti-Nariai and Bertotti-Robinson backgrounds is described. For a vanishing cosmological constant and electromagnetic field, results for well known impulsive pp-waves are recovered.