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

Abstract

Exact solutions for Shapovalov wave spacetimes of type I in Brans–Dicke’s scalar-tensor theory of gravity are constructed. Shapovalov wave spacetimes describe gravitational wave models that allow for the the separation of wave variables in privileged coordinate systems. In contrast to general relativity, the vacuum field equations of the Brans–Dicke scalar-tensor theory of gravity lead to exact solutions for type I Shapovalov spaces, allowing for the the construction of observational tests to detect such wave disturbances. Furthermore, the equations for the trajectories of the test particles are obtained for the models considered.

An Exact Model of a Gravitational Wave in the Bianchi III Universe Based on Shapovalov II Wave Spacetime and the Quadratic Theory of Gravity

“…In our work, we developed an approach to the study of gravitational waves based on Shapovalov wave spacetimes [20][21][22][23] and considered the generalized quadratic theory of gravity with a scalar field, for which the authors had previously obtained an explicit form of the field equations [23]. A model of a gravitational wave in the Bianchi type-III universe, which belongs to the class of Shapovalov type-II wave spacetimes, was considered.…”