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Gravitational lens models with negative convergence(surface mass densityprojected onto the lens plane) inspired by modified gravity theories, exoticmatter and energy have been recently discussed in such a way that a static andspherically-symmetric modified spacetime metric depends on the inverse distanceto the power of positive $n$(n=1 for Schwarzschild metric, n=2 for Elliswormhole) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD87, 027501 (2013)], and it has been shown that demagnification of images couldoccur for $n>1$ lens models associated with exotic matter (and energy), thoughthey cause the gravitational pull on light rays. The present paper considersgravitational lensing shear by the demagnifying lens models and other modelssuch as negative-mass compact objects causing the gravitational repulsion onlight rays like a concave lens. It is shown that images by the lens models forthe gravitational pull are tangentially elongated, whereas those by therepulsive ones are radially distorted. This feature of lensed image shapes maybe used for searching(or constraining) localized exotic matter or energy withgravitational lensing surveys. It is suggested also that an underdense regionsuch as a cosmic void might produce radially elongated images of backgroundgalaxies rather than tangential ones.

Gravitational lensing shear by an exotic lens object with negative convergence or negative mass