Nonlinear Electrodynamics as a symmetric hyperbolic system.

ABALOS, FERNANDO; CARRASCO, FEDERICO; GOULART, ÉRICO; OSCAR REULA

Buenos Aires

Conferencia; Gravitation, Astrophysics, and Cosmology II Argentinian-Brazilian Meeting; 2014

Recent years have witnessed a great activity in nonlinear generalizations of Maxwell´s equations, relevant in different areas of physics. In quantum field theories, the vacuum polarization naturally lead to nonlinear corrections of electromagnetism. Resulting in complicated dispersive media which exhibit almost every phenomenon which is well known from ordinary condensed matter systems. Other contexts where nonlinear electrodynamics (NLE) has been studied are cosmological models, black holes and in the description of the dark sector of the universe. In summary the NLE attracts our attention because it offers deep insights into the important role played by light in experimental and theoretical studies of relativity. Using the geometric formalism of R. Geroch for differential treatment of partial differential equations PDE´s, we show that the equations governing the non-linear electrodynamics, considering arbitrary Lagrangian, are part of the so-called symmetric-hyperbolic systems. Such systems guarantee existence and uniqueness of solutions, as well as the continuity of the initial data; desirable features of any system of equations that point to describe a physical problem. We found that the conditions under which a particular version of the theory is a symmetric hyperbolic system are directly linked to physic propagation cones of that theory. That is, we find that the hyperbolizations found, constitute cones that match the propagation cones of the associated effective metric of these theories.