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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 | | 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. | | Source: | arXiv, gr-qc/0410047 | | Services: | Forum | Review | PDF | Favorites | |
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