GRAVITATIONAL FIELD OF GYRATONS PROPAGATING ON BACKGROUNDS FORMED BY DIRECT-PRODUCT SPACETIMES

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 Plebański–Hacyan universes, conformally flat Bertotti–Robinson and Minkowski spaces. The gyraton solutions are given in a simple Kundt metric form and belong to the class of spacetimes with constant scalar invariants (CSI) of the curvature tensor. The Einstein equations reduce to a set of linear equations on the transverse 2-space which can be explicitly solved using the Green functions.