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

Abstract

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).

4 pages, RevTeX

Cited by in corpus (14)

• Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
• Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem
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• Thirty years of studies of integrable reductions of Einstein's field equations
• Generalized hyperbolic Ernst equations for an Einstein-Maxwell-Weyl field
• New integral equation form of integrable reductions of Einstein equations
• The characteristic initial value problem for colliding plane waves: The linear case
• Gravito-electromagnetic resonances in Minkowski space
• Higher Dimensional Metrics of Colliding Gravitational Plane Waves
• A continuous Riemann-Hilbert problem for colliding plane gravitational waves
• Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
• The stability of Killing-Cauchy horizons in colliding plane wave space-times
• Travelling waves in the expanding spatially homogeneous space-times
• Comment on F.J.Ernst, V.S.Manko and E.Ruiz "On interrelations between Sibgatullin's and Alekseev's approaches to the construction of exact solutions of the Einstein-Maxwell equations" (J.Phys.:Conf.Ser.229(2010)012050; arXiv:1006.5118)