A comparison of approximate gravitational lens equations and a proposal for an improved new one

TL;DR

This paper compares various approximate gravitational lens equations against exact general relativity, proposing an improved version of the Ohanian lens equation that enhances accuracy in modeling light bending.

Contribution

The paper introduces a new expression for the Ohanian lens equation and evaluates its accuracy, highlighting its potential for more reliable gravitational lensing analyses.

Findings

The Ohanian lens equation is the most accurate among common approximations.

The new expression improves the precision of the Ohanian lens equation.

High accuracy is essential for extracting gravitational physics from lensing data.

Abstract

Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.