The Erez-Rosen metric and the role of the quadrupole on light propagation

TL;DR

This paper explores how the quadrupole moment of a static gravitational body affects light propagation, lensing, and image formation, providing analytical solutions and connecting to current astrometric models.

Contribution

It presents an explicit analysis of quadrupole effects on light deflection and lensing using the Erez-Rosen metric, including solutions in the weak field limit.

Findings

Quadrupole moments influence light deflection and lensing observables.

Derived analytical solutions for inverse ray tracing with quadrupole corrections.

Established consistency with existing astrometric models.

Abstract

The gravitational field of a static body with quadrupole moment is described by an exact solution found by Erez and Rosen. Here we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables like image positions and magnification have been explicitly obtained in the weak field and small quadrupole limit. In this limit the spacetime metric appears as the natural generalization to quadrupole corrections of the metric form adopted also in current astrometric models. Hence, the corresponding analytical solution of the inverse ray tracing problem as well as the consistency with other approaches are also discussed.