Particle motion around magnetized black holes: Preston-Poisson   space-time
  We analyze motion of massless and massive particles around black holes immersed in an asymptotically uniform magnetic field and surrounded by some mechanical structure, which provides the magnetic field. The space-time is described by Preston-Poisson metric, which is the generalization of the well-known Ernst metric with a new parameter, tidal force, characterizing the surrounding structure. The Hamilton-Jacobi equations allow separation of variables in the equatorial plane. The presence of tidal force from surroundings considerably changes parameters of the test particle motion: it increases the radius of circular orbits of particles, increases the binding energy of massive particles going from a given circular orbits to the innermost stable orbit near black hole. In addition, it increases the distance of minimal approach, time delay and bending angle for a ray of light propagating near black hole. 
R. A. Konoplya