Optical caustics of Kerr spacetime: the full structure

TL;DR

This paper provides a comprehensive numerical analysis of optical caustics in Kerr spacetime, revealing their shape, size, and image multiplicity across various black hole spins and orientations, confirming analytical predictions and exploring extreme cases.

Contribution

It offers the first exhaustive numerical study of higher order caustics in Kerr black holes, including their shape, size, and behavior at near-extremal spins, extending previous analytical work.

Findings

Caustics maintain a tube shape with astroidal cross-section across parameter space.

Higher order caustics can grow large and wind around the black hole at high spins.

Number of images varies from 2 to 2(n+1) depending on caustic loops.

Abstract

We present an exhaustive numerical investigation of the optical caustics in gravitational lensing by a spinning black hole for an observer at infinity. Besides the primary caustic, we examine higher order caustics, formed by photons performing one or several loops around the black hole. Our investigation covers the whole parameter space, including the black hole spin, its inclination with respect to the line of sight, the source distance, and the caustic order. By comparing our results with the available analytical approximations, we find perfect agreement in their respective domains of validity. We then prove that all caustics maintain their shape (a tube with astroidal cross-section) in the entire parameter space without suffering any transitions to different caustic shapes. For nearly extremal spin, however, higher order caustics grow so large that their cross-sections at fixed radii wind several times around the black hole. As a consequence, for each caustic order, the number of images ranges from 2 to 2(n+1), where n is the number of loops spanned by the caustic. As for the critical curves, we note that for high values of the spin they develop a small dip on the side corresponding to prograde orbits.