The weakly perturbed Schwarzschild lens in the strong deflection limit

TL;DR

This paper analyzes how external gravitational fields weakly perturb the strong deflection gravitational lensing near Schwarzschild black holes, revealing shifts and shapes of caustics and relativistic images.

Contribution

It demonstrates that external perturbations act mainly in the weak field region and describes the resulting changes in relativistic caustics and image formation.

Findings

Relativistic caustics are shifted and become finite diamond shapes.

External perturbations can be treated as weak quadrupole fields.

Sources inside caustics produce four sequences of relativistic images.

Abstract

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.