The collision of plane waves in the general theory of relativity

The problem of colliding plane waves in General Pelativity is discussed and all known exact solutions of the Einstein-Maxwell equations corresponding to various collisions are reviewed. These include collisions involving combinations of electromagnetic and gravitational waves with both collinear and non-collinear polarization. It is pointed out how the collision problem may be simplified by a suitable choice of reference frame. In this way incoming waves approach from spatially opposite directions and the plane symmetry of the waves enable the spacetime to be considered to consist of four regions. One of these regions contains both waves as they interact subsequent to the collision. A solution of the collision problem may be uniquely determined by solving the field equations for this region subject to appropriate junction conditions at the regional boundaries. To facilitate this review, the formalism of Newman and Penrose is utilized and using this it is shown how the field equations may be more appropriately formulated for the treatment of the collision problem. Furthermore, the formalism allows a ready interpretation of the geometry of the spacetime congruences. More precisely, the congruence geometry is described by certain scalar functions which arise in the formalism. The colliding fields may each be considered to define physically a congruence in spacetime and the focussing effect which each field induces on the congruences of the other may then be used to interpret the development of irregularities in the various solutions published.