This thesis describes the collision and subsequent interaction of
two waves which exhibit plane symmetry, according to the theory
of general relativity. The properties of plane waves are discussed
and the necessary field equations and boundary conditions describing
this situation are formulated. Techniques are introduced
by which exact solutions describing the collision of gravitational
waves with constant and aligned polarization may be generated.
By way of demonstrating these techniques, an explicit new solution
is obtained. A complete integral of a family of solutions
which are isomorphic to Gowdy cosmologies is derived, and another
general class of solutions which are the analogue of the
Weyl solutions for axisymmetric space-times is obtained. Exact
solutions are also described for the collision of gravitational waves
with arbitrary polarization when coupled with scalar fields or a
type of null fluid that forms a stiff perfect fluid on interaction. A
method for obtaining large families of solutions of this type from
existing vacuum solutions using either of two potential functions
is introduced, and examples of its application are given. The restriction
of these stiff fluid solutions to the case where the waves
have constant and aligned polarization allows the method to be
A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.
Science and Engineering Research Council award, no. 91000352.