Stationary electromagnetic fields around black holes. III. General solutions and the fields of current loops near the Reissner-Nordström black hole

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Abstract
The stationary multipole solutions of the Einstein-Maxwell equations representing coupled electromagnetic and gravitational perturbations of the extreme Reissner-Nordström black hole are simple rational functions of the radial coordinate. These solutions are used to construct the axially symmetric field of a current loop in the equatorial plane and of a small current loop on the polar axis. The magnetic lines of force are calculated numerically and exhibited graphically. The field representing a general Reissner-Nordström black hole in an asymptotically uniform magnetic field is also given, and its relation to the exact solutions of Ernst describing Kerr-Newman black holes in Melvin's magnetic universe is discussed.