Strong gravitational lensing by compact objects with magnetic dipole

Abstract

Compact objects with magnetic dipole are considered as gravitational lenses. The presence of strong magnetic field near the photon sphere can affect the trajectory of light. We compute the deflection angle near the photon sphere on the equatorial plane of the magnetic dipole. In the Einstein-Maxwell gravity we use the asymptotic metric when a massive object has a magnetic dipole moment. In the Einstein-Born-Infeld gravity we use the effective metric accomodating the nonlinear electrodynamic effect. The deflection angles are expressed as perturbations from the Schwarzschild lensing. As a numerical estimate, we apply the result to a magnetar.