Iterative Approach to Gravitational Lensing Theory
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.
Cite
@article{arxiv.gr-qc/9908082,
title = {Iterative Approach to Gravitational Lensing Theory},
author = {Thomas P. Kling and Ezra T. Newman and Alejandro Perez},
journal= {arXiv preprint arXiv:gr-qc/9908082},
year = {2009}
}
Comments
27 pages, 2 figures, submitted to Phys.Rev.D, minor revisions, new references