Abstract
We consider the propagation of X-ray and gamma ray emissions in strong magnetic and gravitational fields of the pulsar in nonlinear vacuum electrodynamics. We show that the radiation has birefrigence. We have calculated the delay between the two modes, as they propagate from the pulsar to the detecting device. gamma ray astrophysics, pulsar, magnetar, quantum electrodynamics, gravity. We estimate the numerical value of the delay in the case where the magnetic field source is a neutron star with field on a surface B~1016 G (magnetar). Due to the our condition, which must be satisfied for all points of considered beams, our calculation will be applicable only to the beams, for which the pericenter rp exceeds ten radii of the neutron star