Gravitational lenses in arbitrary space-times

TL;DR

This paper introduces a comprehensive formalism for modeling multiple gravitational lenses in arbitrary space-times, enhancing the accuracy of strong-lensing predictions in complex cosmological scenarios.

Contribution

It develops a general framework that unifies various lensing models, allowing for precise calculations in diverse and complex space-time backgrounds.

Findings

Derived a rigorous lens equation for arbitrary space-times.

Provided expressions for amplification and time delays in the new framework.

Applicable to anisotropic cosmologies and beyond tidal regimes.

Abstract

The precision reached by current and forthcoming strong-lensing observations requires to accurately model various perturbations to the main deflector. Hitherto, theoretical models have been developed to account for either cosmological line-of-sight perturbations, or isolated secondary lenses via the multi-plane lensing framework. This article proposes a general formalism to describe multiple lenses within an arbitrary space-time background. The lens equation, and the expressions of the amplification and time delays, are rigorously derived in that framework. Our results may be applied to a wide range of set-ups, from strong lensing in anisotropic cosmologies, to line-of-sight perturbations beyond the tidal regime.