Microlensed image centroid motions by an exotic lens object with
  negative convergence or negative mass
  Gravitational lens models with negative convergence inspired by modified
gravity theories, exotic matter and energy have been recently examined, in such
a way that a static and spherically symmetric modified spacetime metric depends
on the inverse distance to the $n$-th power ($n=1$ for Schwarzschild metric,
$n=2$ for Ellis wormhole, and $n \neq 1$ for an extended spherical distribution
of matter such as an isothermal sphere) in the weak-field approximation
[Kitamura, Nakajima and Asada, PRD 87, 027501 (2013), Izumi et al. PRD 88
024049 (2013)]. Some of the models act as if a convex lens, whereas the others
are repulsive on light rays like a concave lens. The present paper considers
microlensed image centroid motions by the exotic lens models. Numerical
calculations show that, for large $n$ cases in the convex-type models, the
centroid shift from the source position might move on a multiply-connected
curve like a bow tie, while it is known to move on an ellipse for $n=1$ case
and to move on an oval curve for $n=2$. The distinctive feature of the
microlensed image centroid may be used for searching (or constraining)
localized exotic matter or energy with astrometric observations. It is shown
also that the centroid shift trajectory for concave-type repulsive models might
be elongated vertically to the source motion direction like a prolate spheroid,
whereas that for convex-type models such as the Schwarzschild one is
tangentially elongated like an oblate spheroid.
