Mapping weak lensing distortions in the Kerr metric
  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.
