Euler–Heisenberg waves propagating in a magnetic background

Abstract We derive the Euler–Heisenberg solutions that describe electromagnetic waves propagating through very intense uniform magnetic or electric background, with effective metric approach. first explore case of a background: as result interaction between wave and background there is birefringence longitudinal field component arises. The two phase velocities depend on intensity external polarization wave; can be slowed down up to order hundred thousandths for fields $$B/B_\mathrm{cr}<< 1$$ B / cr < 1 . analogous study done when propagates field. then consider situation in movement by means Lorentz boost, modeling magnetized flowing medium. determined how this motion affects speed propagation wave, both direction velocity boost.