The exact time-dependent solution is obtained for a magnetic field growth during a spherically symmetric accretion into a black hole (BH) with a Schwarzschild metric.
Magnetic field is increasing with time, changing from the initially uniform into a quasi-radial field.
Equipartition between magnetic and kinetic energies in the falling gas is supposed to be established in the developed stages of the flow. Estimates of the synchrotron radiation intensity are presented for the stationary flow.
The two-dimensional stationary self-similar magnetohydrodynamic solution is obtained for the matter accretion into BH, in a presence of a large-scale magnetic field, under assumption, that the magnetic field far from the BH is homogeneous. At the symmetry plane perpendicular to the direction of the distant magnetic field, the dense quasi-stationary disk is formed around BH, which structure is determined by dissipation processes.
The radiative efficiency of the magnetized disk is very high, reaching $\sim 0.5\,\dot M\,c^2$. This model of accretion was called recently as a magnetically arrested disk (MAD). Numerical simulations of MAD, and its appearance during accretion into neutron stars are considered and discussed.