Hyperbolicity of Non-linear Electrodynamics

F. CARRASCO; F. ABALOS; E. GOULART; O. REULA

Rio de Janeiro

Congreso; 15th International Conference on Hyperbolic Problems; 2014

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian have a dispersion relation in which propagation planes factor into null planes corresponding to two effective metrics. These metrics share the null directions of the background electromagnetic field at each space-time point. We show that, if the cones these metrics give rise to have a non-empty intersection, then the theory is symmetric hyperbolic. Namely, 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.