Electromagnetic extraction of energy from Kerr black holes

When a rotating black hole is threaded by magnetic field lines supported by external currents flowing in an equatorial disc, an electric potential difference will be induced. If the field strength is large enough, the vacuum is unstable to a cascade production of electron–positron pairs and a surrounding force-free magnetosphere will be established. Under these circumstances it is demonstrated that energy and angular momentum will be extracted electromagnetically. As a further consequence it is shown that charge can never contribute significantly to the geometry of a rotating hole. The fundamental equations describing a stationary axisymmetric magnetosphere are derived and the details of the energy and angular momentum balance are discussed. A perturbation technique is developed which can be used to provide approximate solutions for slowly rotating holes. Solutions appropriate when the field lines threading the hole lie on conical and paraboloidal surfaces at large distances are described to illustrate this mechanism. These ideas are incorporated into a discussion of a model of active galactic nuclei containing a massive black hole surrounded by a magnetized accretion disc. In this model relativistic electrons can be accelerated at large distances from the hole and therefore will not incur serious losses, which is a defect of some existing models. In addition, if the field lines have paraboloidal shape, the energy will be beamed along antiparallel directions as observations of both compact and extended radio sources seem to require.