Particle acceleration around rotating Einstein-Born-Infeld black hole and plasma effect on gravitational lensing

We consider a timelike geodesics in the background of rotating Einstein-Born-Infeld (EBI) black hole to examine the horizon and ergosphere structure. The effective potential that governs the particle's motion in the spacetime and the innermost stable circular orbits (ISCO) is also studied. A qualitative analysis is conducted to find the redshifted ultrahigh center-of-mass (CM) energy as a result of a two-particle collision specifically near the horizon. The recent Event Horizon Telescope (EHT) triggered a surge of interest in strong gravitational lensing by black holes, which provide a new tool comparing the black hole lensing in general relativity and alternate gravity theories. Motivated by this, we also discussed both strong and weakfield gravitational lensing in the space-time discretely for a uniform plasma and a singular isothermal sphere. We calculated the light deflection coefficients (a) over bar and (b) over bar in the strong field limits, and their variance with the rotational parameter a for different plasma frequency as well as in vacuum. For EBI black holes, we found that plasma's presence increases the photon sphere radius, the deflection angle, the deflection coefficients (a) over bar, (b) over bar, the angular positions and the angular separation between the relativistic images. It is also shown that with increasing spin the impact of plasma on a strong gravitational lensing becomes smaller as the spin parameter grows in the prograde orbit (a > 0). For extreme black holes, the strong gravitational effects in the homogenous plasma are similar to those of in a vacuum. We investigate strong gravitational lensing effects by supermassive black holes Sgr A* and M87*. Considering rotating EBI black holes as the lens, we find the angular position of images for Sgr A* and M87* and observe that the deviations of the angular position from that of the analogous Kerr black hole are not more than 2.44 mu as for Sgr A* and 1.83 mu as for M87*, which are unlikely to get resolved by the current EHT observations.