Parameter Estimation of Magnetised Kerr Black Holes Using Their Shadows

Abstract: We investigate the shadow features of magnetized Kerr black holes (MKBHs) using a deviation parameter ( B ) that captures the effect of an external magnetic field on spacetime geometry. These spacetimes, of Petrov type ( D ), are asymptotically non-flat. We use the separability of the Hamilton--Jacobi equation to generate null geodesics and examine the crucial impact parameters for unstable photon orbits that define the black hole shadow. We carefully study how the magnetic field intensity ( B ) and spin parameter ( a ) influence shadow morphology, discovering that increasing ( B ) enlarges the shadow while also introducing additional distortions, especially at high spins. We compute the shadow observables -- area ( A ) and oblateness ( D ) -- and create contour plots in the parameter space [(a/M, \, BM)] to facilitate parameter estimation. We also investigate the dependence of the shadow on observer position, specifically altering the radial coordinate ( r_{\mathrm{O}} ) and inclination angle ( \theta ). The results reveal that as ( B ) increases, so does the shadow size, and the distortion is affected by both spin and observer orientation. For far observers, the shadow approaches its asymptotic shape, but finite-distance observers perceive substantial deviations. Our findings demonstrate that MKBH shadows encode clear imprints of magnetic deviations, thereby offering a potential avenue to distinguish Kerr from non-Kerr spacetimes and to probe magnetic effects in the strong-gravity regime.