Colliding plane impulsive gravitational waves

When two non-interacting plane impulsive gravitational waves undergo a head -on collision, the vacuum interaction region between the waves after the co llision contains backscattered gravitational radiation from both waves. The two systems of backscattered waves each have a family of rays (null geodes ics) associated with them. We demonstrate that if it is assumed that a para meter exists along each of these families of rays such that the modulus of the complex shear of each is equal, then Einstein's vacuum field equations, with the appropriate boundary conditions, can be integrated systematically to reveal the well-known solutions in the interaction region. In so doing, we solve the mystery behind the origin of such solutions. With the use of the field equations, it is suggested that the assumption leading to their i ntegration may be interpreted physically as implying that the energy densit ies of the two backscattered radiation fields are equal. With the use of di fferent boundary conditions this approach can lead to new collision solutio ns.