ALEKSEEV and GRIFFITHS, 1995. Propagation and interaction of gravitational waves in some expanding backgrounds. Physical Review D, 52(8), pp. 4497–4502
An explicit class of solutions is given which represents a family of expanding gravitational waves with distinct wave fronts propagating into a variety of backgrounds, including vacuum Kasner and FRW fluid models with a stiff equation of state. Complete global solutions are given, and it is indicated how solutions describing the collision of such waves may be constructed. Since the solutions obtained are regular apart from the initial singularity, it is concluded that this class of colliding gravitational waves do not introduce singularities into the space-time.