# Mapping weak lensing distortions in the Kerr metric

## TL;DR

This paper develops a new framework for mapping weak gravitational lensing distortions caused by rotating black holes described by the Kerr metric, revealing unique signatures that are currently below observational detection limits.

## Contribution

It introduces a differentiable lensing map in Kerr space-time, extending previous models to account for angular momentum effects on light distortions.

## Key findings

- Identified unique curl-like lensing signatures due to Kerr black holes.
- Quantified the magnitude of Kerr-induced distortions, showing they are below current detection thresholds.
- Extended weak lensing analysis to rotating space-times, enhancing understanding of gravitational lensing in realistic astrophysical scenarios.

## Abstract

Einstein's theory of General Relativity implies that energy, i.e. matter, curves space-time and thus deforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in the case of the Schwarzschild metric, and has been accurately described in the past; however, lensing in the Kerr space-time has received less attention in the literature despite potential practical observational applications. In particular, lensing in such space is not expressible as the gradient of a scalar potential and as such is a source of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiable lensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools of weak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presence of angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-like foreground object on a distribution of background of sources. We verify that the new unique lensing signature is orders of magnitude below current observational bounds for a range of lens configurations.