Nonlinear electrodynamics as a symmetric hyperbolic system
Year: 2015
Type: article
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 pointwise 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 nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] 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.
Authors: Fernando Abalos, Federico Carrasco, Érico Goulart, Oscar Reula
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1531450189