Colliding impulsive waves in succession.

In a recent paper' we have introduced the formulation of the problem of colliding superposed waves in general relativity. Being unable to present an exact solution, we have constructed the proper initial data in the incoming regions. The formation of an essential and therefore impenetrable singularity, however, by the collision of the very first front waves raises the question of whether a physically acceptable solution exists at all. In this Brief Report we consider an arbitrary number of successive impulsive gravitational waves in collision and provide a new approach to this particular problem. The amplitude constants of the waves are chosen in such particular values that the original singularity obtained by Khan and Penrose ' (KP) remains effective. Then, we observe that the original KP geometry is retained in a smaller region of space-time formed by successive waves located at u ( I/&2 (U (1/&2). The reason for this restriction is connected with the fact that for u (U) & I/&2, the spacetime region to be obtained (as described below) falls beyond the essential singularity u + v = 1, and therefore such incoming waves can be handled only within the context of an exact solution. A globally exact solution is beyond our scope and this handicap compels us to explore the possible validity of the KP solution for such a sequence of incoming waves.