Primary caustics and critical points behind a Kerr black hole

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.

7 pages, 5 figures; v2: extended discussion, 2 figures added, results unchanged; in press on PRD

References in corpus (4)

• Strong deflection limit of black hole gravitational lensing with arbitrary source distances
• Analytical Kerr black hole lensing in the weak deflection limit
• Magnification relations for Kerr lensing and testing Cosmic Censorship
• Kinematic effect in gravitational lensing by clusters of galaxies

Cited by in corpus (10)

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• Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses
• Weak and strong deflection gravitational lensings by a charged Horndeski black hole
• The role of Lambda in the cosmological lens equation
• Optical caustics of Kerr spacetime: the full structure
• On aberration in gravitational lensing
• Relativistic effects cannot explain galactic dynamics
• Wavefronts and Light Cones for Kerr Spacetimes
• Examining the Kerr Metric through Wave Fronts of Null Geodesics
• Kerr black holes as circular polarizers