The Erez–Rosen metric and the role of the quadrupole on light propagation
Donato BiniAstronomical Observatory of Torino, INAF, via Osservatorio 20, I-10025 Pino Torinese (TO), ItalyMariateresa CrostaAstronomical Observatory of Torino, INAF, via Osservatorio 20, I-10025 Pino Torinese (TO), ItalyFernando de FeliceAndrea GeralicoInternational Center for Relativistic Astrophysics (ICRA), University of Rome ‘La Sapienza’, I-00185 Rome, ItalyAlberto VecchiatoAstronomical Observatory of Torino, INAF, via Osservatorio 20, I-10025 Pino Torinese (TO), Italy
2013en
ABI
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.
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