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

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.

arXiv comment33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravity

References in corpus (6)

• Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation
• Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves
• Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies
• Monodromy Transform Approach to Solution of Some Field Equations in General Relativity and String Theory
• New integral equation form of integrable reductions of Einstein equations
• The characteristic initial value problem for colliding plane waves: The linear case

Cited by in corpus (10)

• Electromagnetic fields in curved spacetimes
• An exact smooth Gowdy-symmetric generalized Taub-NUT solution
• Gravito-electromagnetic resonances
• Gravito-electromagnetic resonances in Minkowski space
• Electromagnetic potentials in curved spacetimes
• Asymptotics to all orders of the Euler--Darboux equation in a triangle
• Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
• A continuous Riemann-Hilbert problem for colliding plane gravitational waves
• The stability of Killing-Cauchy horizons in colliding plane wave space-times
• Travelling waves in the expanding spatially homogeneous space-times