Gravitational lensing shear by an exotic lens object with negative
  convergence or negative mass
  Gravitational lens models with negative convergence(surface mass density
projected onto the lens plane) inspired by modified gravity theories, exotic
matter and energy have been recently discussed in such a way that a static and
spherically-symmetric modified spacetime metric depends on the inverse distance
to the power of positive $n$(n=1 for Schwarzschild metric, n=2 for Ellis
wormhole) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD
87, 027501 (2013)], and it has been shown that demagnification of images could
occur for $n>1$ lens models associated with exotic matter (and energy), though
they cause the gravitational pull on light rays. The present paper considers
gravitational lensing shear by the demagnifying lens models and other models
such as negative-mass compact objects causing the gravitational repulsion on
light rays like a concave lens. It is shown that images by the lens models for
the gravitational pull are tangentially elongated, whereas those by the
repulsive ones are radially distorted. This feature of lensed image shapes may
be used for searching(or constraining) localized exotic matter or energy with
gravitational lensing surveys. It is suggested also that an underdense region
such as a cosmic void might produce radially elongated images of background
galaxies rather than tangential ones.
