Analytical Kerr black hole lensing in the weak deflection limit

Abstract

We present an analytical treatment of gravitational lensing by a Kerr black hole in the weak deflection limit. Lightlike geodesics are expanded as a Taylor series up to and including third-order terms in $m/b$ and $a/b$, where $m$ is the black hole mass, $a$ the angular momentum, and $b$ the impact parameter of the light ray. Positions and magnifications of individual images are computed with a perturbative analysis. At this order, the degeneracy with the translated Schwarzschild lens is broken. The critical curve is still a circle displaced from the black hole position in the equatorial direction and the corresponding caustic is pointlike. The degeneracy between the black hole spin and its inclination relative to the observer is broken through the angular coordinates of the perturbed images.