Gravitational lens optical scalars in terms of energy-momentum distributions

TL;DR

This paper derives new, gauge-invariant formulas for gravitational lensing optical scalars and deflection angles based on energy-momentum tensor components, generalizing previous models with broader applicability.

Contribution

It introduces general expressions for lensing quantities in terms of energy-momentum distributions, relaxing previous restrictive assumptions and providing a versatile approximation method.

Findings

New gauge-invariant expressions for optical scalars and deflection angles

Generalized formulas applicable to arbitrary matter distributions

A flexible approximation method for solving lens equations

Abstract

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.