Primary caustics and critical points behind a Kerr black hole

Understand

The primary optical caustic surface behind a Kerr black hole is a four-cusped tube displaced from the line of sight.

• We derive the caustic surface in the nearly asymptotic region far from the black hole through a Taylor expansion of the lightlike geodesics up to and including fourth-order terms in m/b and a/b, where $m$ is the black hole mass, a the spin and b the impact parameter.
• The corresponding critical locus in the observer's sky is elliptical and a point-like source inside the caustics will be imaged as an Einstein cross.
• With regard to lensing near critical points, a Kerr lens is analogous to a circular lens perturbed by a dipole and a quadrupole potential.