In this letter we will investigate the possibility whether primordial black holes can grow to become galactic black holes or not. We find that even a primordial black hole with the probable maximum mass cannot grow in a short timescale. Only a hole with the initial mass of order ∼104M⊙ ∼104M⊙ can significantly grow to become a galactic hole.

An axisymmetric, stationary electrodynamic model of the central engine of an active galactic nucleus has been well formulated by Macdonald and Thorne. In this model the relativistic region around the central black hole must be filled by highly conducting plasma. We analyze plasma wave propagation in this region and discuss the results. We find that the ionosphere cannot exist right outside of the event horizon of the black hole. Another interesting aspect is that certain resonance phenomena can occur in this case.

An axisymmetric, stationary electrodynamic model of the central engine of an active galactic nucleus has been well formulated by Macdonald and Thorne. In this model the relativistic region around the central black hole must be filled by highly conducting plasma and the equations of magnetohydrodynamics are then satisfied. In this paper we analyze magnetohydrodynamic wave propagation in this region. We find that there are three distinct types of waves - the Alfven wave and two magnetosonic waves. The wave equations turn out to be not very different from those in nonrelativistic case except they are redshifted.

It has been suggested that there could be a large number of primordial black holes which were formed in the early universe. We analyze the growth of such a primordial black hole following two different accretion rates - the Eddington accretion rate and the Bondi accretion rate - at the center of a host star like the sun. We find that a primordial black hole with M < ∼ 10 17 g cannot substantially grow in any case throughout the lifetime of a host star. If M > ∼ 10 17 g , the evolution of a host star depends entirely on the mode of accretion, but it ends as a black hole in either case. Since more stars may have primordial black holes at the center of a galaxy this may result in a cluster of such black holes, and the cluster may eventually collapse to produce a single supermassive black hole.

Rapid progress in modern computer industries now enables us to solve the Einstein equations numerically. In the first part of this paper we briefly review how to deal with those equations in relativistic astrophysics and cosmology. In the second part we introduce two examples-the Centrella and Wilson's cosmology and the Shapiro and Teukolsky's relativistic stellar cluster.

The original axisymmetric, stationary electrodynamic model of the central engine in an active galactic nucleus proposed by Macdonald and Thorne consists of a supermassive black hole with magnetic field lines that pass through the region just outside the event horizon of the black hole. Each magnetic field line rotates with a constant angular velocity which will exceed the speed of light at large radii. Even though the field lines are purely mathematical entities this condition sets a stringent physical constraint on the motion of the magnetic field lines and the particles on them. In this paper we will show that we can remove this auxiliary constraint in our model by allowing nonstationary processes. As a result the magnetic field lines can be twisted and wound up in a region lying outside of the quasi-stationary magnetosphere of the black hole. We conclude that astrophysical jets are formed in that region due to the twisted and wound magnetic field lines powered by the Blandford-Znajek process and the other driving forces.