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

TL;DR

This paper investigates gravitational lensing effects around rotating black holes in Eddington-inspired Born-Infeld (EiBI) gravity, analyzing both strong and weak field regimes and how parameters like charge, spin, and correction terms influence observable lensing features.

Contribution

It provides the first detailed analysis of equatorial lensing for EiBI black holes, including numerical and analytical results on impact parameters, deflection angles, and image magnifications, extending understanding beyond general relativity.

Findings

Lensing parameters depend strongly on charge, spin, and correction term.

Relativistic image positions and magnifications are computed for EiBI black holes.

Weak lensing parameters vary with charge and correction terms.

Abstract

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 $\epsilon$.