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Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

G. A. Alekseev·J. B. Griffiths
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Abstract

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.

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G. A. Alekseev, J. B. Griffiths. 2004-10-11. Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem. https://doi.org/10.1088/0264-9381%2F21%2F23%2F021

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