Abstract
Spacetimes which represent the interaction of two plane asymptotic waves are defined, and shown to be a more realistic generalisation of colliding plane waves. For the case of collinear polarisation, general asymptotic waves, restricted by the criterion that they have bounded amplitudes at their caustics, generically produce an unavoidable curvature singularity. The results are first illustrated by a class of exact solutions. The methods used apply equally to colliding plane waves.
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