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.

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. In this paper we analyze the axisymmetric, nonstationary electrodynamics of the black hole magnetosphere in a similar way. In the earlier papers we employed the poloidal component of the plasma velocity which is confined only to the radial direction of the cylindrical coordinate system. In this paper we employ a more general poloidal velocity and get the Grad-Shafranov equation of the force-free magnetosphere of a Kerr black hole. The equation is consistent with the previous ones and is more general in many aspects as it should be. We also show in more general approaches that the angular velocity of the magnetic field lines anchored on the accreting matter tends to become close to that of the black hole at the equatorial zone of the hole.

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.

Variability of active galactic nuclei is now a well-known phenomenon. This remains to be fully explained by a theoretical model of the central engine. Time scales of AGN variability seem to range continuously from hours up to months. The short time scale variability must be related to the phenomena on the event horizon of the black hole, while the long one to those in the accretion disk or surrounding matter. Based on the axisymmetric, nonstationary model of the central engine, we discuss theoretical considerations on the variability of active galactic nucleus.

In the previous work we made a long term evolution code for the central black hole in an active galactic nucleus under the assumption that the Blandford-Znajek process is the source of the emission. Using our code we get the evolution of the angular velocity of the precession for a supermassive black hole. We consider a hole at the center of an axisymmetric, ellipsoidal galactic nucleus. Our numerical results show that, only for the cases such that the stellar density or the mass of the black hole is large enough, the precession of the black hole - presumably the precession of the galactic jet - is interestingly large.

Variability of the emission-line spectra of active galactic nuclei is now a well-known phenomenon. This remains to be fully explained by a theoretical model of the central engine in an active galactic nucleus. Since the magnetic field lines are anchored on the accreting matter, they continuously fall on the event horizon of the central supermassive black hole and increase the net field strength of the hole magnetosphere. The field strength, however, cannot increase without an upper limit and, therefore, it will be decreased by some unknown processes. In this paper we discuss that these increasing and decreasing modes can be repeated periodically and explain the variability of power output, therefore, variability of active galactic nuclei.

Sexual dimorphism is the most conspicuous difference between the sexes. This study examines possible sexual dimorphism and the relative growth patterns of morphometric characteristics in the marine medaka, Oryzias dancena for their potential to help differentiate between males and females of this species. The von Bertalanffy growth parameters estimated by a non-linear regression method were L∞=30.2 mm, K=3.22/year, and τ0=-0.05. All 18 characteristics measured showed a difference between males and females from 70 days after hatching. Each of these characteristics were significantly different between sexes (ANCOVA, P<0.05), and the ratio of standard length between sexes showed that males were larger than females for all five morphometric measurements. Fin length measurements were taken for 21 distances of anal fin and 7 distances of dorsal fin between landmarks. There were all differences for all dorsal fin rays between the males and the females and there is significant difference in 70 days after their hatch when the sexual dimorphism is presented. The significant difference (P<0.05) in fin ray for male and female was more greatly seen as they grow. Male marine medaka showed more rapid growth than females, with longer length, dorsal fins and anal fins. Differences in these characteristics will be useful during experiments when it is necessary to differentiate between sexes of marine medaka.