The force-free magnetosphere of a black hole

The magnetic field plays an essential role in extracting energy from a rotating black hole. We consider the structure of stationary axisymmetric force-free black hole magnetospheres using the "3 + 1" formalism. The structure can be characterized by three scalar functions - the stream function, the current potential and the angular velocity of the magnetic field lines. We discuss the possible analytic solutions to tile equations governing those scalar functions. From one such solution that can represent tile electromagnetic field configuration in the spat:e with an accretion disk on the Equatorial plane of the black hole, we estimate tile amount of tile electric charge induced on the stretched horizon of the black hole.