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

We consider a time-like geodesics in the background of rotating Einstein-Born-Infeld (EBI) black hole to examine horizon and ergosphere structure. The effective potential that governs particle's motion spacetime innermost stable circular orbits (ISCO) is also studied. A qualitative analysis conducted find redshifted ultrahigh centre-of-mass (CM) energy as result two-particle collision specifically near horizon. recent Event Horizon Telescope (EHT) triggered surge interest strong gravitational lensing by holes, which provide new tool comparing general relativity alternate gravity theories. Motivated this, we discussed both weak-field space-time discretely for uniform plasma singular isothermal sphere. calculated light deflection coefficients $\bar{a}$ $\bar{b}$ field limits, their variance with rotational parameter $a$ different frequency well vacuum. For EBI found plasma's presence increases photon sphere radius, angle, $\bar{a}$, $\bar{b}$, angular positions separation between relativistic images. It shown increasing spin impact on becomes smaller grows prograde orbit ($a>0$). extreme effects homogenous are similar those investigate supermassive holes Sgr A* M87*...