Chaotic shadow of a non-Kerr rotating compact object with quadrupole
  mass moment
  We have studied numerically the shadows of a non-Kerr rotating compact object
with quadrupole mass moment, which belongs to Manko-Novikov family. The
non-integrable photon motion caused by quadrupole mass moment affects sharply
the shadow of the compact object. As the deviation parameter related to
quadrupole mass moment is negative, the shadow of compact object is prolate and
there are two disconnected main shadows with eyebrows located symmetrically on
both sides of the equatorial plane. As the deviation parameter is positive, the
shadow becomes oblate and the main shadow is joined together in the equatorial
plane. Moreover, in this positive cases, there is a disorder region in the left
of shadow which increases with the quadrupole-deviation parameter.
Interestingly, we also find that Einstein ring is broken as the deviation from
Kerr metric is larger than a certain critical value. This critical value
decreases with the rotation parameter of black hole. Especially, the observer
on the direction of rotation axis will find some concentric bright rings in the
black disc. Finally, supposing that the gravitational field of the supermassive
central object of the galaxy described by this metric, we estimated the
numerical values of the observables for the black hole shadow.
