Numerical study of the deflection of a light beam passing through the magnetosphere of a magnetar under the influence of gravity and nonlinear electrodynamics of vacuum

This study presents a review of numerical methods for investigating the combined effects of nonlinear vacuum electrodynamics and gravity on the propagation of electromagnetic radiation through a magnetar's magnetosphere. Within the framework of the Born-Infeld model of nonlinear electrodynamics, numerical solutions to the system of effective geodesic equations derived from the effective metric defined via the Penrose-Newman formalism are analyzed. The initial conditions are based on the parameters of a gamma-ray burst that passed near the closest magnetar to Earth. The system is solved numerically using the Runge-Kutta method. The study examines the bending of electromagnetic rays near the magnetar, their angular distribution, front deformation, and anisotropy in the energy density distribution. It is found that the radiation deflects by more than 86 degrees near the magnetar's surface. The wavefront shape transforms into an ellipse, and anisotropic propagation is observed near the compact object. Additionally, the energy density of the radiation increases by a factor of 1.83 as it passes through the combined field of the magnetar. These results characterize the behavior of electromagnetic radiation in strong combined fields near compact objects and provide important insights for future astrophysical observations and theoretical modeling.