Primary caustics and critical points behind a Kerr black hole

TL;DR

This paper analytically derives the shape and properties of primary caustics behind a Kerr black hole, revealing their structure and implications for gravitational lensing near supermassive black holes.

Contribution

It provides a detailed Taylor expansion-based analytical description of Kerr black hole caustics and critical points, extending understanding of gravitational lensing effects.

Findings

Caustic surface is a four-cusped tube displaced from the line of sight.

Critical locus in the sky is elliptical, producing Einstein cross images.

Kerr lensing resembles a circular lens with dipole and quadrupole perturbations.

Abstract

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. The caustic structure of the supermassive black hole in the Galactic center could be probed by lensing of low mass X-ray binaries in the Galactic inner regions or by hot spots in the accretion disk.