Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

Details Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

2004-10-11

arxiv.org/abs/gr-qc/0410047v1

Class.Quant.Grav.21:5623-5654,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/21/23/021

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.

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