The Bianchi identity and weak gravitational lensing

Abstract

We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing. Using the spin coefficient formalism of Newman and Penrose [1962], we show that certain complex components of the Weyl and Ricci curvature tensors are directly related to fundamental observables in weak gravitational lensing. In the case of weak gravitational fields, we then show that the Bianchi identity provides a field equation for the Ricci tensor assuming a known Weyl tensor. From the Bianchi identity, we derive the integral equation for weak lensing presented by Miralda-Escude [1996], thus making the Bianchi identity a first principles equation of weak gravitational lensing. This equation is integrated in the important case of an axially symmetric lens and explicitly demonstrated in the case of a point lens and a SIS model.

accepted to CQG

References in corpus (6)

• Weak Gravitational Lensing
• Probing the Universe with Weak Lensing
• An Exact Universal Gravitational Lensing Equation
• Fermat Potentials for Non-Perturbative Gravitational Lensing
• Image distortion from optical scalars in non perturbative gravitational lensing
• Image distortion in non perturbative gravitational lensing

Cited by in corpus (5)

• Gravitational lens optical scalars in terms of energy-momentum distributions
• Expressions for optical scalars and deflection angle at second order in terms of curvature scalars
• Poisson equation for weak gravitational lensing
• A connection between linearized Gauss-Bonnet gravity and classical electrodynamics II: Complete dual formulation
• Angular diameter distances reconsidered in the Newman and Penrose formalism