Imprints of magnetic charge on the particle orbits, weak gravitational lensing and black hole shadows

We present a comprehensive analysis of a magnetically charged black hole solution featuring its distinctive physical properties and dynamical evolution. By investigating test particle orbits, we derive crucial quantities like the energy, angular momentum, innermost stable circular orbit radius, photon sphere, and Lyapunov exponent. This encompasses research into weak gravitational lensing phenomena in vacuum and plasma medium, focusing on the uniform plasma distribution under SIS and NSIS profiles. Additionally, the amplification of black hole images is studied, with a cross-verification of the deflection angle formula via the Gibbons-Werner method in the optical geometry scheme. A critical feature of our solution is the charge parameter $q$ and coupling constant $\mu$, and distinguishes this solution from the classical Schwarzschild black hole. We also study the shadow of a magnetically charged black hole, with an emphasis on the impact of the magnetic charge $q$ and the coupling constant $\mu$. Both the shape and the size of the shadow are found to differ significantly from the Schwarzschild case. The higher values of $q$ and $\mu$ produce larger deviations. Observations of black hole shadows are thus found to provide detectable indications of magnetic charge. Lastly, we study the stability of a newly magnetically charged black hole by analyzing the Lyapunov factor. Our results provide novel geometrical interpretations for the effect of non-trivial electromagnetic and coupling structures on black hole metrics, as well as their consequences for astrophysical observations and the testing of alternative theories of gravity.