Equatorial and quasi-equatorial gravitational lensing by Kerr black hole pierced by a cosmic string

In the present paper, we study numerically the equatorial lensing and quasiequatorial lensing by Kerr black hole pierced by a cosmic string in the strong deflection limit. We calculate the strong deflection limit coefficients and the deflection angle, which are found to depend closely on the cosmic string parameter $\beta$ and dimensionless spin $a_{*}$. The magnification and positions of relativistic images are also computed in the strong deflection limit and a two-dimensional lens equation is derived. The most important and outstanding effect is that the caustics drift away from the optical axis and shift in the clockwise direction with respect to the Kerr black hole. For fixed $a_{*}$ of the black hole, the caustics drift farther away from the optical axis for a large value of $\beta$. And for fixed $\beta$, they drift farther for high $a_{*}$. We also obtain the intersections of the critical curves with the equatorial plane, which decrease with $a_{*}$ and $\beta$. In particular, we obtain a quantity $\bar{\mu}_{k+1}/\bar{\mu}_{k}$, which is independent of the black hole spin and mass. Thus, through measuring it, one is allowed to determine the value of $\beta$ from astronomical observations.