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16 September 2019
 
  » arxiv » gr-qc/0410047

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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 ;
Date 11 Oct 2004
Journal Class.Quant.Grav. 21 (2004) 5623-5654
Subject General Relativity and Quantum Cosmology; Exactly Solvable and Integrable Systems | gr-qc hep-th nlin.SI
AbstractWe 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.
Source arXiv, gr-qc/0410047
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