Deflection of Light in the Equatorial Plane of the Kerr Black Hole: From the Last Photon Orbit to Infinity

Series expansions for the bending of light in the equatorial plane of a Kerr black hole are given for the strong and weak deflection limits with various values of the spin parameter ranging from zero to one. From the exact bending angle expression, with no known analytical solution, we get power series approximations for the bending angle in terms of the impact parameter of the incident light ray. Analytical expressions allow us to obtain various pieces of information for images formed in gravitational lensing. Specifically, the asymmetry that arises in the spin-dependent shifts in image positions can be predicted by the analytical expansions. We apply our results for the case of a galactic supermassive black hole to predict angular shifts of relativistic images from the optic axis. The possible observation of the asymmetric image shifts with telescopes can only be predicted with the perturbative expansions in the strong deflection regime.