Dynamics of Fermat potentials in non-perturbative gravitational lensing

TL;DR

This paper introduces a comprehensive framework using null-surface formulation of general relativity to analyze Fermat potential dynamics in non-perturbative gravitational lensing, including thick lenses and gravitational waves.

Contribution

It develops a general, approximation-free approach to gravitational lensing, deriving new lens equations for thick lenses and gravitational wave lensing.

Findings

Derived lens equations for thick compact lenses and gravitational waves.

Framework removes the thin-lens approximation in gravitational lensing.

Applicable to generic, non-perturbative gravitational scenarios.

Abstract

We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we derive two lens equations: one for the case of thick compact lenses and the other one for lensing by gravitational waves. These equations in principle generalize the astrophysical scheme for lensing by removing the thin-lens approximation while retaining the weak fields.