The existence of galaxies indicates that the early universe must have been inhomogeneous and might have been highly chaotic. This could have lead to regions of the size of the particle horizon undergoing gravitational collapse to produce black holes with initial masses from 10-5 g upwards. Radiation pressure in the early Universe would cause these black holes to grow by accretion. However, despite previous expectations, this accretion would not be very much unless the initial conditions of the Universe were arranged in a special and a causal manner. Observations indicate that, at the most, only a small fraction of the matter in the early Universe can have undergone gravitational collapse.

It is argued that for black holes of mass less than roughly 1017 g formed in the early Universe, the accretion process must be calculated using quantum mechanics. It is also argued that primordial black holes must be more massive than 1017 g if they are to possess charge.

Surface composition of a neutron star in the absence of accretion is pure iron (Tsuruta, 1964). We considered two cases of accretion. (a) The accretion of inter-stellar matter: Here we expect the presence of a significant amount of various elements between proton and iron, though iron is still the most dominant. (b) The accretion as the energy source of an X-ray source in a binary system. Here it is most likely that the incoming flux is sufficiently high (non-steady state) and protons accumulate on the accreting region of the surface.

Two generation mechanisms of magnetic fields in pulsars are considered.

If the temperature of a star is more than 108K, the star consists of a normal fluid of neutrons, protons and electrons. Because the angular velocity of pulsars is not constant dω/dt ≠0, inertia effects can occur, and generate magnetic fields through the relative motion of charged particles with different masses. The kinematic viscosity of electrons is 30 times larger than that of protons; hence electrons move with the crust, but the proton-neutron fluid will move relative to the electrons. The magnetic momentum can be calculated by the following formula where Meff = Mp + Mn(Nn/Np), R = radius of the star, σ = conductivity. For typical neutron stars we have dω/dt~ 10-8 s-2, R~106 cm, σ~1029 s-1 and we get a magnetic field of the order of 1010 G.

Working in the signature (+ + + -) and units such that G = 1 = c, it was found a solution of Einstein-Maxwell equations with λ (without current and pseudo-current). In real coordinates xμ=(p, σ, q, τ) the solutions is: (1)(2) where (3) is pure imaginary; in (1) ‘d’ denotes the external differential]. Not all constants m0, n0, e0, g0, b, ∊, λ are physically significant: by re-scaling coordinates ∊ can be made equal to +1,0, or −1. The solution is of the type D: the double Debever-Penrose vectors (4) have the common complex expansion Z = (q + ip)-1. Among C(a)'s only C(3) given by: (5) is in general ≠0. The invariants of the electromagnetic field are: (6)

We found new, stationary axisymmetric, asymptotically flat exact solutions to Einstein's vacuum field equations, which are classified by an integer δ and Kerr metric is the solution of δ = 1. The number of ring singularity on the equatorial plane is δ. The odd δ metrices contain the surfaces of event horizon but the even δ metrices do not. Except the Kerr metric, however, the space-time becomes singular at the poles on these surfaces.

A five parameter solution of the combined Einstein-Maxwell equations is given which describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds, and angular momentum. The solution is asymptotically flat and has a singular infinite red shift surface. Possible relevance of the solution to black hole physics is discussed.

The physics of spherically symmetrical accretion onto a compact object is briefly reviewed. Neither neutron stars nor stellar-mass black holes are likely to be readily detectable if they are isolated and accreting from the interstellar medium. Supermassive black holes in intergalactic space may however be detectable. The effects of accretion onto compact objects in binary systems are then discussed, with reference to the phenomena observed in variable X-ray sources.

During accretion of plasma in binary systems containing compact objects magnetic fields are most likely to become arranged quickly, grow and fully determine the disk structure. The disk divides into separate dense clots, and a corona appears over the equatorial plane of the system. In the corona magnetic lines of force reconnect and beams of relativistic particles are generated.