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

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