Wave-like spatially homogeneous models of Stackel spacetimes (2.1) type in the scalar-tensor theory of gravity

TL;DR

This paper derives six exact solutions for wave-like, spatially homogeneous models in scalar-tensor gravity, revealing explicit forms of scalar fields, metric functions, and test particle actions within these cosmological models.

Contribution

It introduces new exact solutions for wave-like scalar-tensor cosmological models, including explicit scalar and metric functions, expanding understanding of such spacetimes.

Findings

Six exact solutions obtained for scalar-tensor wave-like models

Explicit forms of scalar fields and metric functions provided

Solutions classified as Bianchi type III and Petrov type N

Abstract

Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like space-time models allow the existence of privileged coordinate systems where the eikonal equation and the Hamilton-Jacobi equation of test particles can be integrated by the method of complete separation of variables with the separation of isotropic (wave) variables on which the space metric depends (non-ignored variables). An explicit form of the scalar field and two functions of the scalar field that are part of the general scalar-tensor theory of gravity are found. The explicit form of the eikonal function and the action function for test particles in the considered models is given. The obtained solutions are of type III according to the classification Bianchi and type N according to the classification of Petrov.