Since Einstein's equations are essentially nonlinear, gravitational fields and waves cannot be simply superposed. In general relativity, even electromagnetic waves experience a nonlinear interaction through the gravitational equations, in spite of the fact that Maxwell's equations remain linear. The physical phenomena that arise as a result of this nonlinearity need to be understood. And the simplest situation for which this can be modelled exactly is in the collision and subsequent interaction of plane waves in a flat Minkowski background. In fact, many explicit solutions are now known which describe situations of this type. Thorough reviews of early work on this topic can be found in the book by Griffiths (1991) and also in Chapter 25 of Stephani et al. (2003). The purpose of the present chapter is to use an up-to-date approach to review the basic results that have been found, with a particular emphasis on the physically significant features that arise. It will also be shown how certain solutions that have been studied in previous chapters reappear in this context.

Clearly, the collision of plane waves, is a highly idealised situation. Realistic waves have convex wavefronts, and only become approximately planar at a large distance from their source. Moreover, exact plane waves are infinite in transverse spatial directions and therefore have unbounded energy. These features may have unfortunate consequences in exact colliding plane wave space-times. Thus, when seeking to interpret these solutions, care has to be taken to distinguish properties that apply to general wave interactions from those that arise as a consequence of the idealised assumptions.