Deflection of light by magnetars in the generalized Born–Infeld electrodynamics

Abstract

We study the deflection of light by a magnetic dipole field in the generalized Born–Infeld electrodynamics. Using the effective index of refraction and the trajectory equation based on geometric optics, we compute the weak bending angle of light passing on the equator of the magnetic dipole. In the limit where the classical Born–Infeld parameter is infinite, the bending angle agree with the one computed from the Euler–Heisenberg Lagrangian. We also compute the bending angle using the geodesic equation of the effective metric induced by a massive object with magnetic dipole. In the massless limit the bending angle agrees with the computation using the trajectory equation. We apply the result to magnetars to estimate the order of magnitude for the bending angle.