Image distortion in nonperturbative gravitational lensing

Abstract

We introduce the idea of shape parameters to describe the shape of the pencil of rays connecting an observer with a source lying on his past light cone. On the basis of these shape parameters, we discuss a setting of image distortion in a generic ͑exact͒ spacetime, in the form of three distortion parameters. The fundamental tool in our discussion is the use of geodesic deviation fields along a null geodesic to study how source shapes are propagated and distorted on the path to an observer. We illustrate this nonperturbative treatment of image distortion in the case of lensing by a Schwarzschild black hole. We conclude by showing that there is a nonperturbative generalization of the use of Fermat's principle in lensing in the thin-lens approximation.

The Bianchi identity and weak gravitational lensing

“…Frittelli & Newman [8] first pointed out that the lens should be coded into a space-time metric, and then solving the null geodesic equations would simultaneously give the "time of flight" equation and lens mapping. In a two-paper set, Frittelli et al [9] related general relativity's optical scalars to the "shears" and "convergences" cited in the thin-lens literature. These papers also wrote out integral relations that showed how image distortion grew continuously along the pencil of rays connected a source and observer.…”

“…Frittelli et al [10] shows how these quantities are related to the convergence (ρ) and shear (σ) in general relativity. For this paper, it is critical to note the similarities that κ has with Φ 00 and that Ψ 0 has with λ and µ.…”

“…Strong lensing and general image distortion have been studied by several researchers including Frittelli & Newman [8] and two connected papers by Frittelli et al [9,10] with a substantial review provided by Perlick [11]. This paper is the first paper that seeks a first principles equation for observational weak lensing.…”

Image distortion from optical scalars in nonperturbative gravitational lensing

“…2 (Readers familiar with [2] may want to skip this section). A non-perturbative approach to distortion requires, as a fundamental tool, a non-perturbative lens mapping: a mapping from the image location to the source location that does not rely on weak-field nor thin-lens regimes.…”

Strong lensing, plane gravitational waves and transient flashes

“…χ represents the angle between the principal axes of that ellipse and the Sachs basis. D ± and χ are referred as shape parameters [1,43].…”