Kerr black hole lensing for generic observers in the strong deflection limit

TL;DR

This paper analytically studies gravitational lensing by a Kerr black hole for generic observers, revealing how observables depend on the black hole's spin projection and emphasizing the need for high-precision measurements to distinguish spin and inclination.

Contribution

It extends previous Kerr black hole lensing models to include generic observer positions and provides analytical expressions up to second order in spin, enhancing understanding of relativistic images.

Findings

Observables depend on the projection of the black hole spin.

Higher-order corrections are needed to distinguish spin from inclination.

Accurate VLBI measurements are essential for parameter determination.

Abstract

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.