A number of exact solutions of Einstein's equations are obtained, which describe the collision and subsequent interaction of two plane parallel waves. Gravitational waves, null electromagnetic fields, and neutrino fields are all considered with collisions between any two types. It is shown that two such waves mutually focus each other with the focus usually appearing as a singularity in space-time. Further conclusions are made regarding the qualitative nature of the interactions, and it is argued that these also apply in more realistic physical situations.
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The physical situation under consideration in this work is that of the collision and interaction of two waves. The waves considered may be gravitational, electromagnetic, or neutrino. In classical theory two such waves pass through each other with any interaction. However, in the general theory of relativity, the field equations are nonlinear, so that solutions can not be superposed and interactions between waves occur. It is hoped that some of the features of this nonlinearity will be shown by a consideration of the collisions between plane waves.
It is obviously of greater relevance physically to consider collisions between realistic waves with curved wavefronts, although such fields may be approximated by plane waves .at large distances from their sources. The main reason, however, for restricting attention here to the study of plane waves is that exact solutions describing the interactions are available. In the last few years, exact solutions describing colliding gravitational waves, electromagnetic waves, and neutrinos have been given. The qualitative nature of these solutions is here considered in greater detail. New solutions are also given here describing collisions between different types of waves which may be gravitational, electromagnetic, or neutrino. The emphasis throughout is on the qualitative aspects of the interactions, since it may be hoped that these effects are also present in the interactions between waves in more realistic situations.