Effect of Birefringence of Electromagnetic Radiation in the Field of a Relativistically Rotating Pulsar or Magnetar within the Framework of Nonlinear Vacuum Electrodynamics

Within the framework of parameterized post-Maxwellian vacuum electrodynamics, the propagation of an X-ray and gamma radiation pulse through the electromagnetic field of a relativistically rotating pulsar is investigated. Expressions are obtained for the trajectory of this pulse and for the law of its motion from the point $$\mathbf{r}_{s}=\{x_{s},y_{s},z_{s}\},$$ where at the moment of time $$t=t_{s}$$ an X-ray or gamma-ray burst occurs, to the point $$\mathbf{r}_{d}=\{x_{s},y_{s},z_{d}\},$$ where the detector of this radiation is located. In the case when the post-Maxwellian parameters of the theory differ, $$\eta_{1}\neq\eta_{2}$$ , the time of nonlinear electrodynamic delay of electromagnetic signals carried by different normal modes is calculated. The change in the polarization state of the X-ray or gamma radiation pulse after passing through the electromagnetic field of a relativistically rotating pulsar is analyzed. The possibilities of observing the nonlinear effect of the electromagnetic field of a relativistically rotating pulsar on X-ray and gamma-ray pulses are discussed.