Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe

To construct a dynamical model of gravitational waves, a method of proper times of test particles in a background gravitational field is proposed. Analytical models of secondary gravitational waves are constructed as perturbative solutions of linearized field equations against the background of an exact wave solution of Einstein’s equations for the vacuum in a Bianchi VI universe in a preferred wave coordinate system. An analytical form for the components of the secondary gravitational wave metric is found from compatibility conditions for the field equations. From the field equations, an explicit form of ordinary differential equations is obtained for the functions included in small corrections to the metric for secondary gravitational waves. Analytical solutions are obtained. It is shown that there exists a continuum of gravitational wave parameters for which the perturbative solutions are stable.