We study magnetic field topologies and magnetic field strength in a thin accretion disk around a rotating black hole. The magnetic field is assumed to enter the disk at the outer edge and is amplified in the accretion process by differential rotation. This scenario seems likely for AGN, where magnetized plasma from a molecular torus flows into an inner accretion disk.
In nonideal Newtonian magnetohydrodynamics the presence of a rotating central black hole is taken into account by using the form of the Keplerian rotation law valid for Kerr geometry outside the marginally stable orbit and a boundary layer, caused by the frame dragging effect, within. In the unstable region close to the hole the turbulent timescale is much larger than the accretion timescale so that the effective magnetic diffusivity, which is large in the disk due to turbulence, is low. As a consequence the poloidal magnetic field lines cross the horizon almost radially in agreement with .
We present stationary axisymmetric solutions of the induction equation for vanishing α-effect. Dipolar field structures are most favourable for the generation of fast jets and can effectively contribute to the heating of a corona or some X-ray source. Quadrupolar field structures may also drive jets, however the field strength is considerably lower and therefore also the energy that can be supplied into a corona or a jet.