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 point-like. The degeneracy between the black hole spin and its inclination relative to the observer is broken through the angular coordinates of the perturbed images.

12 pages; minor changes to match the version in press on Phys. Rev. D

References in corpus (3)

• Kerr black hole lensing for generic observers in the strong deflection limit
• The weakly perturbed Schwarzschild lens in the strong deflection limit
• Analytical formulas for gravitational lensing

Cited by in corpus (9)

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• On the influence of the cosmological constant on gravitational lensing in small systems
• The role of Lambda in the cosmological lens equation
• Optical caustics of Kerr spacetime: the full structure
• Magnification relations for Kerr lensing and testing Cosmic Censorship
• Primary caustics and critical points behind a Kerr black hole
• Strong gravitational lensing from compact bodies: analytical results
• Kinematic effect in gravitational lensing by clusters of galaxies
• On aberration in gravitational lensing