Comparative Studies of Lensing Methods

TL;DR

This paper compares standard thin lens, iterative, and exact gravitational lensing methods in simple test cases, showing the iterative approach often yields higher accuracy, but certain simplified models can produce significant errors.

Contribution

It introduces and evaluates an iterative gravitational lensing method, demonstrating its improved accuracy over the thin lens approximation in specific scenarios.

Findings

Iterative method outperforms thin lens approximation in accuracy.

Thin lens and iterative methods are highly accurate for single and double monopole lenses.

Simplified two-lens models can lead to large inaccuracies in realistic situations.

Abstract

Predictions of the standard thin lens approximation and a new iterative approach to gravitational lensing are compared with an ``exact'' approach in simple test cases involving one or two lenses. We show that the thin lens and iterative approaches are remarkably accurate in predicting time delays, source positions and image magnifications for a single monopole lens and combinations of two monopole lenses. In the cases studied, the iterative method provided greater accuracy than the thin lens method. We also study the accuracy of a ``2 lens, single lens plane model,'' where two monopole lenses colinear with the observer are modeled by a mass distribution in a single lens plane lying between them. We see that this model can lead to large inaccuracies in physically meaningful situations. A previous version of this paper was published as Phys.Rev.D62, 024025, (2000) with errors in the computation of two lens comparisons. This paper corrects these errors and presents new conclusions which differ from the previous version.