Spacetime Perspective of Gravitational Lensing in Perturbed Cosmologies

TL;DR

This paper introduces a spacetime-based approach to gravitational lensing in cosmological models, providing more accurate methods than the traditional thin lens approximation by analyzing geodesics and wave front singularities.

Contribution

It develops a comprehensive spacetime framework for gravitational lensing in perturbed cosmologies, replacing the thin lens approximation with methods grounded in general relativity.

Findings

Derived integral expressions for geodesics in perturbed cosmologies

Explained observed image shapes using the Jacobian of the lens mapping

Demonstrated development of wave front singularities and time delays

Abstract

We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral expressions which are used to examine the formation of multiple images and the observed shapes of non-point sources. We develop the lens mapping from the spacetime perspective, and use the Jacobian of the mapping to explain the observed image shapes. Approaching the geodesic equations as ordinary differential equations, we demonstrate the development of wave front singularities and time delays between light ray signals. This work demonstrates that the widely used thin lens approximation can be replaced with more robust techniques aligned with general relativity.