Exact models of pure radiation in R2 gravity for spatially homogeneous wave-like Shapovalov spacetimes type II

Presented are exactly integrable models with pure radiation in R2 gravity with a cosmological constant related to wave-like Shapovalov spacetimes type II. Spatially homogeneous models of Shapovalov spacetimes were considered. The obtained solutions belong to spaces of type III according to the Bianchi classification and of type N according to the Petrov classification. For the models under consideration, exact solutions for the equations of motion of test particles are obtained in the Hamilton-Jacobi formalism. For the obtained exact models, solutions of the geodesic deviation equations are obtained.