Perturbative Approach to the Gravitational Lensing by a Non-spherically
  Distorted Compact Object
  We investigate the gravitational lens effect caused by a non-spherically
distorted compact object. The non-spherical property of the gravitational
potential is modeled by a quadrupole moment. Under the assumption that the
quadrupole contribution is small, we solve perturbatively the lens equation and
obtain the image positions and the amplification factors. We show that the
separation angle of two major images is only slightly changed by the existence
of the quadrupole contribution, whereas the difference of the amplification
factors may be significantly modified. Our results indicate that even a tiny
non-spherical distortion of the lens potential may cause significant amount of
flux anomalies in the lensed images.
