We consider the collisions of plane gravitational and electromagnetic waves with
distinct wavefronts and of arbitrary polarizations in a Minkowski background. We
first present a new, completely geometric formulation of the characteristic initial
value problem for solutions in the wave interaction region for which initial data are
those associated with the approaching waves. We present also a general approach to
the solution of this problem which enables us in principle to construct solutions in
terms of the specified initial data. This is achieved by re-formulating the nonlinear
dynamical equations for waves in terms of an associated linear problem on the
spectral plane. A system of linear integral “evolution” equations which solve this
spectral problem for specified initial data is constructed. It is then demonstrated
explicitly how various colliding plane wave space-times can be constructed from
given characteristic initial data.
This pre-print has been submitted, and accepted, for publication in the journal, Classical and quantum gravity. The definitive version: ALEKSEEV, G.A, and GRIFFITHS, J.B., 2004. Collision of plane gravitational and electromagnetic
waves in a Minkowski background: solution of the
characteristic initial value problem. Classical and quantum gravity, 21(23),pp.5623-5654 is available at www.blackwell-synergy.com.