Image distortion from optical scalars in non perturbative gravitational lensing

TL;DR

This paper presents an alternative method to describe image distortion in non-perturbative gravitational lensing using optical scalars and their evolution along null geodesics, linking distortion parameters to spacetime curvature.

Contribution

It introduces a new approach to analyze shape and distortion parameters in gravitational lensing through optical scalars and optical equations, complementing previous vector-based methods.

Findings

Derived relations between distortion parameters and optical scalars.

Connected optical scalars to spacetime curvature via optical equations.

Provided a framework for analyzing image distortion in gravitational lensing.

Abstract

In a previous article concerning image distortion in non-perturbative gravitational lensing theory we described how to introduce shape and distortion parameters for small sources. We also showed how they could be expressed in terms of the scalar products of the geodesic deviation vectors of the source's pencil of rays in the past lightcone of an observer. In the present work we give an alternative approach to the description of the shape and distortion parameters and their evolution along the null geodesic from the source to the observer, but now in terms of the optical scalars (the convergence and shear of null vector field of the observer's lightcone) and the associated optical equations, which relate the optical scalars to the curvature of the spacetime.