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Gravitational lensing in Tangherlini spacetime in the weak gravitational field and the strong gravitational field

The gravitational lensing effects in the weak gravitational field by exotic lenses have been investigated intensively to find nonluminous exotic objects. Gravitational lensing based on 1/r^n fall-off metric, as a one-parameter model that can treat by hand both the Schwarzschild lens (n=1) and the Ellis wormhole (n=2) in the weak field, has been recently studied. Only for n=1 case, however, it has been explicitly shown that effects of relativistic lens images by the strong field on the light curve can be neglected. We discuss whether relativistic images by the strong field can be neglected for n>1 in the Tangherlini spacetime which is one of the simplest models for our purpose. We calculate the divergent part of the deflection angle for arbitrary n and the regular part for n=1, 2 and 4 in the strong field limit, the deflection angle for arbitrary n under the weak gravitational approximation. We also compare the radius of the Einstein ring with the radii of the relativistic Einstein rings for arbitrary n. We conclude that the images in the strong gravitational field have little effect on the total light curve and that the time-symmetric demagnification parts in the light curve will appear even after taking account of the images in the strong gravitational field for n>1.