Causal Structure and Birefringence in Nonlinear Electrodynamics
  We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also proof that there is only one analytic nonlinear electrodynamics presenting no birefringence. 
C. A. M. de Melo, L. G. Medeiros and P. J. Pompeia
hep-th gr-qc hep-ph math-ph math.MP