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

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.

24 pages, 8 figures; published version

References in corpus (3)

• Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
• A general relativistic model for the light propagation in the gravitational field of the Solar System: the dynamical case
• Microlensing modulation by quadrupole variation

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