  For the strong gravitational wave model, an explicit transformation is
obtained from a privileged coordinate system with a wave variable to a
synchronous reference frame with separation of time and space variables. In a
synchronous reference frame, a general form of the gravitational wave metric,
solutions to the equations of trajectories for test particles in the
Hamilton-Jacobi formalism, a solution to the eikonal equation for radiation,
and a form of equations for the light cone of an observer in a gravitational
wave were found. Using the obtained relations, the form the retarded time of
radiation in the gravitational wave was found. The general relations obtained
can be applied both in Einstein general theory of relativity and in modified
theories of gravity. The obtained relations were applied in the work for an
exact model of a gravitational wave in the Bianchi type VI universe based on an
exact solution of Einstein vacuum equations.
