Solving the Characteristic InitialValue Problem for Colliding Plane Gravitational and Electromagnetic Waves
Abstract
A method is presented for solving the characteristic initialvalue problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromytransform approach to fields with nonanalytic behavior 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 wave fronts).
 Publication:

Physical Review Letters
 Pub Date:
 November 2001
 DOI:
 10.1103/PhysRevLett.87.221101
 arXiv:
 arXiv:grqc/0105029
 Bibcode:
 2001PhRvL..87v1101A
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 4 pages, RevTeX