The Gravitational Lens Equation for Embedded Lenses; Magnification and Ellipticity

TL;DR

This paper derives a new gravitational lens equation for embedded lenses within a flat universe, accounting for the deflector's integration into the mean density, and compares it with standard lensing theory to evaluate corrections.

Contribution

It introduces a novel lens equation for embedded lenses and provides an iterative solution scheme, highlighting differences from conventional linear lensing models.

Findings

Derived the embedded lens equation for point mass condensations.

Developed an iterative method to solve the new lens equation.

Quantified corrections to magnification and ellipticity due to embedding.

Abstract

We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean.