Nonlinear electrodynamics as a symmetric hyperbolic system

Abstract

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.

References in corpus (5)

• Cosmological Effects of Nonlinear Electrodynamics
• No compelling cosmological models come out of magnetic universes which are based in nonlinear electrodynamics
• Thermodynamics of Born-Infeld Black Holes
• Parameter estimation of a nonlinear magnetic universe from observations
• Fractional Effective Action at strong electromagnetic fields

Cited by in corpus (24)

• Well-posed formulation of Lovelock and Horndeski theories
• High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics
• Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
• Cherenkov radiation from the quantum vacuum
• On causality in nonlinear vacuum electrodynamics of the Plebański class
• Black holes in nonlinear electrodynamics: quasi-normal spectra and parity splitting
• Covariant Hyperbolization of Force-free Electrodynamics
• On the compatibility of Nonlinear Electrodynamics models with Robinson--Trautman geometry
• Nonlinear electrodynamics is skilled with knots
• On the ill posedness of Force-Free Electrodynamics in Euler Potentials
• Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure
• Effects of non-linear vacuum electrodynamics on the polarization plane of light
• Photon traps in nonlinear electrodynamics
• Entropy bounds and nonlinear electrodynamics
• Light propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws
• A necessary condition for strong hyperbolicity of general first order systems
• Degenerate behavior in nonlinear vacuum electrodynamics
• Well-posed formulation of Einstein-Maxwell effective field theory
• On constraint preservation and strong hyperbolicity
• Mimicking a rotating black hole with nonlinear electrodynamics
• Bekenstein Inequalities and Nonlinear Electrodynamics
• Remarks on the algebraic structure of (2, 2) double forms
• Metric-Induced Principal Symbols in Nonlinear Electrodynamics
• Propagation features of Lorentz-violating electrodynamics