Signals and discontinuities in general relativistic nonlinear electrodynamics

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Abstract
A theory of nonlinear electrodynamics in an arbitrary curved space–time is developed from the fundamental action functional for a charged perfect fluid. The equations for small perturbations on a fixed nonlinear background are then the initial point for a comprehensive study of the characteristic surfaces. The essential distinctions between linear and nonlinear electrodynamic interactions under the influence of gravitation are exhibited. Discontinuities in the first derivatives of small perturbations are encountered (1) which may be of general algebraic types for both the electrodynamic and gravitational fields and (2) which may have spacelike propagation. A specific set of constraints which would permit the propagation of these extraordinary radiative fronts is presented. If the physical organization of a particular problem is presumed to be sufficiently sensitive to the nonlinear nature of the dynamical interactions, then the application of traditional causal concepts may be unreliable when intuition derived from Maxwellian electrodynamics with noninteracting photons is anticipated to provide event horizons.

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