Second order Kerr deflection

We perform a full second order calculation of the deflection of light along the equatorial plane in the Kerr metric. Previous Kerr deflection calculations were interested in obtaining the correction due to rotation to the Einstein deflection. By expanding to first order in the rotational parameter a, they obtain the Einstein deflection of 4M/r _o and the second order deflection due to rotation of , (where r _o is the point of closest approach). In this paper, we are interested in going beyond the rotational contribution for the purpose of astrophysical applications. We therefore keep all terms up to second order in our final weak field expansion. Besides the rotational contribution, we also obtain an extra second order term of . Since M > a, this extra term is greater than the rotational contribution of in astrophysical applications. When a/M is close to unity the terms are of the same order of magnitude.