Gyratons on direct-product spacetimes

TL;DR

This paper derives exact gyraton and gravitational wave solutions on specific direct-product spacetimes, expanding the understanding of such solutions in algebraic type II backgrounds with constant scalar invariants.

Contribution

It introduces explicit gyraton solutions on direct-product and type D spacetimes, including Nariai and Bertotti-Robinson universes, using a simplified Kundt metric form.

Findings

Solutions are explicitly constructed using Green functions.

The Einstein equations reduce to linear equations on the transverse space.

The solutions include well-known universes like Nariai and Bertotti-Robinson.

Abstract

We present and analyze exact gyraton and nonexpanding gravitational wave solutions of algebraic type II on backgrounds which are a direct-product of two 2-spaces of constant curvature, or more general type D spacetimes. This family of electro-vacuum background spacetimes contains the Nariai, anti-Nariai and Plebanski-Hacyan universes, conformally flat Bertotti-Robinson and Minkowski spaces. The gyraton solutions are given in a simple Kundt metric form. They belong to the recently discussed class of spacetimes with constant scalar invariants (CSI) of the curvature tensor. We show that the Einstein equations reduce to a set of linear equations on the transverse 2-space which can be explicitly solved using the Green functions.