Colliding plane gravitational waves of unequal strength

Khan and Penrose, and separately Szekeres, presented solutions of colliding impulsive and sandwich plane gravitational waves, respectively. They only considered equal strength waves, which would impart no momentum to test particles in their path on the plane of collision at the time. We had earlier probed both spacetimes using the pseudo-Newtonian ( ψ N) formalism. In neither case was it really clear what parameter represented the “strength” of the wave. In this paper we identify the required parameter and extend the colliding sandwich plane gravitational wave solution to unequal strengths. Since the impulsive plane waves of Khan and Penrose correspond to a limit of the sandwich waves with the pulse duration tending to zero, we have used the procedure to obtain the generalization of the Khan–Penrose solution to unequal strengths. The resulting spacetimes are exact solutions of vacuum field equations.