Iterative Approach to Gravitational Lensing Theory

TL;DR

This paper introduces an iterative method for gravitational lensing theory applicable to various space-times, providing a new way to approximate null geodesics and relate to existing models.

Contribution

It presents a novel iterative approach to gravitational lensing that works near known solutions, bridging approximate and exact formulations.

Findings

Developed iterative gravitational lens equations for Schwarzschild space-time

Demonstrated the method's applicability to different cosmological models

Connected the iterative approach with standard and exact lensing formulations

Abstract

We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.