Image distortion in non perturbative gravitational lensing

TL;DR

This paper introduces a non-perturbative framework using shape and distortion parameters to analyze image distortion caused by gravitational lensing in exact spacetimes, exemplified by Schwarzschild black holes.

Contribution

It develops a novel, exact approach to describe gravitational lensing distortions without relying on perturbation theory, extending Fermat's principle to the thin-lens approximation.

Findings

Defines shape parameters for source images.

Formulates distortion parameters for generic spacetimes.

Applies the framework to Schwarzschild black hole lensing.

Abstract

We introduce the idea of {\it shape parameters} to describe the shape of the pencil of rays connecting an observer with a source lying on his past lightcone. On the basis of these shape parameters, we discuss a setting of image distortion in a generic (exact) spacetime, in the form of three {\it 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 non-perturbative treatment of image distortion in the case of lensing by a Schwarzschild black hole. We conclude by showing that there is a non-perturbative generalization of the use of Fermat's principle in lensing in the thin-lens approximation.