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Solving the characteristic initial-value problem for colliding plane gravitational and electromagnetic waves

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preprint
posted on 17.01.2006, 10:32 by G.A. Alekseev, Jerry Griffiths
A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The cruxof the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (“dynamical”) monodromy data which evolve from data specified on the initial characteristics (the wavefronts).

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  • Science

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  • Mathematical Sciences

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120382 bytes

Publication date

2001

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This is a pre-print. The definitive version: GRIFFITHS, G.A. and ALEKSEEV, J.B., 2002. Solving the characteristic initial-value problem for colliding plane gravitational and electromagnetic waves. Physical Review, 87(22), Art. No. 221101, at: http://prl.aps.org/.

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en

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