The influence of uniform magnetic fields on strong field gravitational lensing by Kerr black holes

Abstract We examine gravitational lensing strong deflection limit (SDL) by magnetized Kerr black holes (MKBHs), which are accurate Kerr-Bertotti-Robinson solutions for Kerr black holes in a uniform magnetic field with additional magnetic field strength B apart from mass m and spin a . Unlike Kerr-Melvin spacetimes, the MKBH geometry is Petrov type D, without conical singularities, allowing photons to reach asymptotic infinity and making the concept astrophysically feasible. We use the SDL formalism to compute the photon sphere radius, critical impact parameter, deflection angle, and lensing observables, including the image position θ ∞ , angular separation s , and relative magnification r mag , as well as their relationships with the parameters a and B . Our results reveal that the relativistic image's photon sphere and angular size increase with B for prograde orbits as well as retrograde orbits, whereas lensing observables deviate significantly from the Kerr scenario. For M87*, the angular position of relativistic images ranges from 8.67 μas to 26.58 μas for B = 0.1, and the time delay between the first two images increases from 158.5 h to 159.6 h for prograde orbits, while decreases from 380.8 h to 340.8 h for retrograde orbits, respectively, at B = 0.1 and | a |=0.9. Similarly, for Sgr A*, the image position has a range 11.47 μas to 35.38 μas for B = 0.1, with time delays enhanced by approximately 0.04 min for prograde orbits, while a reduction in time delay of 1.57 min for retrograde orbits, respectively, at B = 0.1 and | a |=0.9. The relative magnification r mag ranges from 0.926 to 8.845 at B = 0.1. Our outcomes suggest strong gravitational lensing as a powerful tool to investigate the magnetic fields around astrophysical black holes, and in particular, we demonstrate that the MKBH spacetime enables constraints on the parameters a and B .