Optical and thermodynamic properties of Kerr-Bertotti-Robinson black holes

Abstract

We investigate the thermodynamic and optical properties of Kerr--Bertotti--Robinson black holes, namely rotating black holes immersed in an external Bertotti--Robinson electromagnetic background. In the fixed-$a$ ensemble, we derive the horizon mass relation, the Hawking temperature, the entropy, the Helmholtz-type free energy, the heat capacity, and the extremal remnant configuration. These quantities reduce smoothly to their Kerr counterparts as $B\to0$. In the weak-field regime, the leading thermodynamic corrections arise at order $B^2$; the extremal radius is shifted at this order, whereas the remnant mass receives its first correction only at order $B^4$. We also introduce a formal AdS-like thermodynamic interpretation of the Bertotti--Robinson scale, treating the associated pressure as an effective response variable rather than a genuine cosmological pressure. Because the spacetime is not asymptotically flat, we further compute the finite-radius Komar mass and the Komar charge associated with the horizon generator. Using the Hamilton--Jacobi formalism, we derive the separated null-geodesic potentials, the impact parameters of spherical photon orbits, and the celestial coordinates of the shadow boundary for a finite-distance observer. We then characterize the photon-region boundaries, ergosphere thickness, photon--ergosphere gap, shadow area, and magnetic shadow susceptibility. Within the perturbative regime considered, the Bertotti--Robinson background decreases the averaged ergosphere thickness and shadow area, increases the photon--ergosphere gap, and produces a negative shadow susceptibility whose magnitude is enhanced by rotation.