The Influence of Uniform Magnetic Fields on Strong Field Gravitational Lensing by Kerr Black Holes

Abstract: We investigate strong gravitational lensing using 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 previous magnetized spacetimes, the MKBH geometry is Petrov type D, devoid of conical singularities, allowing photons to reach asymptotic infinity and making the concept astrophysically feasible. We use the strong deflection limit formalism to calculate the photon sphere radius, critical impact parameter, deflection angle, and lensing observables including the image position $\theta_\infty$, angular separation $s$ and relative magnification $r_{\text{mag}}$, 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 $B$, whereas lensing observables deviate significantly from the Kerr scenario. For M87*, with $a=0.9$, the angular position of relativistic images increases from $10.8~\mu$as (Kerr) to $12.02~\mu$as, and the time delay between the first two images increases from $158.5$ h to $176$ h at $B=0.4$. Similarly, for Sgr A*, the image position increases from $14.4~\mu$as to $16~\mu$as, with time delays enhanced by approximately $0.7$ minutes. The relative magnification $r_{\text{mag}}$ grows with $B$ and deviates by $0.53$ from Kerr black holes at $B=0.4$. Our findings highlight strong gravitational lensing as a powerful tool to probe the presence of magnetic fields around astrophysical black holes, and in particular, we demonstrate that the MKBH spacetime enables constraints on the parameters $a$ and $B$.