Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity

Abstract

All classes of spatially homogeneous spacetime models in the generalized scalar–tensor theory of gravitation are found to allow the integration of the equations of motion of test particles and the eikonal equation by the method of separation of variables by type (3.1). Three classes of exact solutions are obtained that relate to Shapovalov wave-like spacetime models. The resulting spacetime models are of types IV, VI and VII according to the Bianchi classification and type [Formula: see text] according to Petrov classification.

Quadratic Theory of Gravity with a Scalar Field and Type I Shapovalov Wave Spacetimes

“…Previously, we obtained the exact models of gravitational waves with pure radiation related to Shapovalov spacetimes of type I in Einstein's theory [26] and a number of wave solutions of other types in scalar-tensor and quadratic theories of gravity [27][28][29][30][31].…”

“…The general properties of the energy-momentum tensor of pure radiation in wave spacetime models that allow the separation of variables in the eikonal equation were considered by us earlier in [38]. Wave models were considered earlier Shapovalov spacetimes of type II [27][28][29] and for Shapovalov spacetimes of type III [30], where exact models of gravitational waves in scalar-tensor theories of gravity were constructed.…”

Type I Shapovalov Wave Spacetimes in the Brans–Dicke Scalar-Tensor Theory of Gravity

“…As Shapovalov [13,14] showed, the scalar equation can be integrated by separating the variables in the same privileged coordinate systems as the Hamilton-Jacobi equation. Therefore, the use of Shapovalov wave spaces also provides additional opportunities for the exact solution of the scalar equation [26][27][28][29]. Recently, new results have also been obtained in the study of the symmetries of the Klein-Gordon-Fock equations.…”

Type I Shapovalov wave spacetimes in the Brans-Dicke scalar-tensor theory of gravity

“…As Shapovalov [17,18] showed, the scalar equation can be integrated by separation of variables in the same privileged coordinate systems as the Hamilton-Jacobi equation. Therefore, the use of Shapovalov wave spaces also provides additional possibilities for the exact solution of the scalar equation [30][31][32][33]. Recently, in the study of the symmetries of the Klein-Gordon-Fock equations, new results have also been obtained [34][35][36][37].…”