Plane Gravitational Waves in Spatially-Homogeneous Models of type-(3.1) Stäckel Spaces

Abstract

A classification is performed of the spaces with plane-wave metrics in accordance with the presence of three-dimensional subgroups of the group of space-time motion with three-dimensional spatial orbits. In order to obtain spatially-homogeneous models, exact solutions to Einstein’s vacuum equations are found. To obtain these solutions, the Petrov and Bianchi classifications are performed. The results obtained on the classification of the plane-wave metrics using the assumed or three-dimensional subgroups of the group of motion with three-dimensional spatial orbits can be used for any metric gravitational theories.