Gravitational lensing for stationary axisymmetric black holes in Eddington-inspired Born-Infeld gravity

The recent years witnessed a surge of interest of the lensing of the black holes arising from general as well as other modified theories of gravity due to the experimental data available from the EHT results. The EHT may open a new door indicating the possible existence of the rotating black hole solutions in modified theories of gravity in the strong field regime. With this motivation, we investigate in the present paper the equatorial lensing $(\theta=\pi/2)$ by a recently obtained exact rotating black holes solution in EiBI theory in both the strong and weak field limits. Such black holes are the modification of Kerr-Newman black holes in general relativity, characterized by their mass ($M$), the charge ($Q$), and the rotation parameter ($a$). and an additional term $\epsilon$ accounting for the correction to the Kerr-Newman solutions. We show numerically the variations of the impact parameter $u_m$, the light deflection coefficients $p$ and $q$, the total azimuthal bending angle $\alpha_D$ and find a close dependence of these quantities on the charge parameter $r_q$, the correction term $\epsilon$ and the spin $a$. We also calculate the angular position $\theta_\infty$, and the angular separation $s$, and the magnification of the relativistic images. In addition, we also discuss the weak lensing of the black holes in EiBI theory using the Gauss-Bonnet theorem. We calculate the weak lensing parameter and find its variation with different values of the parameters $r_q$ and $\epsilon$.