Metric of a Slow Rotating Body with Quadrupole Moment from the Erez-Rosen Metric

TL;DR

This paper derives a metric for a slowly rotating body with a quadrupole moment using perturbation methods on the Erez-Rosen metric, aiming to improve relativistic astrometry and gravitational lensing models.

Contribution

It introduces a new metric incorporating slow rotation and quadrupole effects into the Erez-Rosen metric for better astrophysical modeling.

Findings

Derived a perturbative metric for rotating bodies with quadrupole moments.

Applicable to relativistic astrometry and gravitational lensing.

Enhances modeling accuracy for astrophysical objects.

Abstract

A metric representing a slowly rotating object with quadrupole moment is obtained using a perturbation method to include rotation into the weak limit of the Erez-Rosen metric. This metric is intended to tackle relativistic astrometry and gravitational lensing problems in which a quadrupole moment has to be taken into account.