Solution for "geodesic" motion of a Schwarzschild black hole along a magnetic field in AdS2 x S2 space-time

The exact solution of Einstein - Maxwell equations for a Schwarzschild black hole immersed in the static spatially homogeneous AdS${}^2\times {\mathbb{S}}^2$ space-time of Bertotti-Robinson magnetic universe is presented. In this solution, the black hole possesses a finite initial boost in the direction of the magnetic field and performs a “geodesic” oscillating motion interacting with the background gravitational and electromagnetic fields.