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

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 $$1/\beta ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>β</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> 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.