Deflection of light by a compact object with electric charge and magnetic dipole in Einstein-Born-Infeld gravity

TL;DR

This paper analyzes how light bends around a charged, magnetized compact object within Einstein-Born-Infeld gravity, deriving the effective metric and calculating the light deflection angle considering nonlinear electromagnetic effects.

Contribution

It introduces a novel calculation of light deflection in Einstein-Born-Infeld theory accounting for both electric and magnetic fields, including nonlinear electromagnetic effects.

Findings

Derived the effective metric considering nonlinear electromagnetic effects.

Calculated the light bending angle including electric and magnetic fields.

Presented limiting cases for pure electric or magnetic fields.

Abstract

We consider the bending of light around a compact astrophysical object with both the electric field and the magnetic field in Einstein-Born-Infeld theory. From the null geodesic of a light ray passing a massive object with electric charge and magnetic dipole, the effective metric was obtained from the light cone condition reflecting the nonlinear electromagnetic effects. We found the asymptotic form of the effective metric up to the first order in gravitational constant $G$ and Born-Infeld parameter $1/\beta^2$ on the equatorial plane. Then we compute the bending angle of light from the geodesic equation. The result includes particular cases where only one type of field is present taking the appropriate limits.