Parameter estimation of Kerr-Bertotti-Robinson black holes using their shadows

Abstract

We investigate the shadow of Kerr-Bertotti-Robinson black holes (KBRBHs), which have a deviation parameter $B$ that captures the effect of an external magnetic field on the spacetime geometry. These spacetimes of Petrov type $D$ are asymptotically non-flat. We utilise 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 investigate how the magnetic field strength $B$ and spin parameter $a$ influence black hole shadows, discovering that increasing $B$ increases the shadow size while also introducing additional distortions, especially at high spins. We calculate the shadow observables, viz., area $A$ and oblateness $D$ and create contour plots in the parameter space $(a, B)$ to facilitate parameter estimation. We also investigate the dependence of the shadow on the observer's position, specifically by altering the radial coordinate $r_O$ and the inclination angle $\theta$. For far viewers, the shadow approaches its asymptotic shape, but finite-distance observers perceive substantial deviations. The energy emission rate analysis reveals that the magnetic field parameter $B$ modifies the Hawking radiation spectrum, with increasing $B$ suppressing emission via backreaction, which lowers the Hawking temperature. Our findings confirm that KBRBH shadows encode 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.