In this review article the famous 'jet equation' in a Minkowski magnetosphere around the compact objects will be fully derived for the pedagogical purposes.

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary black hole magnetosphere in this paper. We concentrate on deriving the ‘Grad-Shafranov equations’; both in the force-free and non-force-free cases. In the time-independent limit our equations naturally coincide with stationary equations as they should.

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary force-free black hole magnetosphere and the motion of the plasma. We concentrate on deriving the totally new equations for the entropy incrrease and the angular momentum, energy extraction of the black hole.

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary force-free black hole magnetosphere and the motion of the plasma. We concentrate on deriving the relations between the velocity components of the plasma and those of the accreting magnetic field lines. We conclude that the former are given by the sum of the latter and the magnetic field terms.

In this review article the famous 'jet equation' of the neutron stars and black holes will be fully derived for the pedagogical purposes.

In this paper, we simplify the equations of the Macdonald-Thome black hole magnetosphere. Our major assumption is that the 3-D electric and magnetic flux isosurfaces respectively form families of confocal oblate spheroids and hyperboloids. As a result, the magnetospheric equations are greatly simplified, and may provide a useful framework for instances when rigorous, theoretical approaches are not necessary.

In this review article we introduce the 'H-R diagram' of black holes. Some fundamental concepts of black hole thermodynamics and electrodynamics are also summarized in detail.

Since Goldreich and Julian's pioneering work in 1969, the pulsar magnetosphere theory has been dramatically developed for theorists to possess an elegant axisymmetric, stationary model. Based on this development the black hole magnetosphere theory has also been established in the last 30 years. Such theoretical developments will be reviewd equation by equation in this paper.

We derive the Grad-Shafranov equation in the Macdonald-Thorne magnetosphere of the super-massive black hole in an active galactic nucleus. Our major assumption is that the plasma velocity is not only toroidal but also poloidal. As a result, we get the correction terms which are related to the poloidal motion of plasma like electrodynamic jets.

The Blandford-Znajek process, which extracts the rotational energy of the supermassive black hole at the center of an active galactic nucleus, is now well explained and educated through the electronic circuit analysis established by Macdonald and Thorne. The Macdonald-Thorne circuits consist of the batteries and resistances of the central black hole and the astrophysical region around the accretion disk. In this letter we will consider the possibility whether we can connect coils and condensers in such circuits or not. If possible, that may explain a sudden corona-phenomenon in an active galactic nucleus. We conclude that a flash of order ~5×1040ergss−1 can occur around a \~109M⨀ \~109M⨀ black hole through this process.