We study the strong gravitational lensing in the background of a rotating
non-Kerr compact object with a deformed parameter ϵ and an unbound
rotation parameter a. We find that the photon sphere radius and the
deflection angle depend sharply on the parameters ϵ and a. For the
case in which the black hole is more prolate than a Kerr black hole, the photon
sphere exists only in the regime ϵ≤ϵmax for prograde
photon. The upper limit ϵmax is a function of the rotation
parameter a. As ϵ>ϵmax, the deflection angle of the light
ray closing very to the naked singularity is a positive finite value, which is
different from those in both the usual Kerr black hole spacetime and in the
rotating naked singularity described by Janis-Newman-Winicour metric. For the
oblate black hole and the retrograde photon, there does not exist such a
threshold value. Modelling the supermassive central object of the Galaxy as a
rotating non-Kerr compact object, we estimated the numerical values of the
coefficients and observables for gravitational lensing in the strong field
limit.Comment: 16 pages, 10 figures. The corrected version to be appeared in Phys.
Rev.