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

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

2001-05-08

arxiv.org/abs/gr-qc/0105029v1

Phys.Rev.Lett.87:221101,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, RevTeX

Scientific paper

10.1103/PhysRevLett.87.221101

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 crux of 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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