ACCRETION IN A KERR BLACK-HOLE MAGNETOSPHERE - ENERGY AND ANGULAR-MOMENTUM TRANSPORT BETWEEN THE MAGNETIC-FIELD AND THE MATTER

We study a magnetohydrodynamic (MHD) interaction between accreting matter and magnetic field in a stationary and axisymmetric magnetosphere surrounding a Kerr black hole which will exist in active galactic nuclei. The critical condition that the MHD ingoing flows must pass through the fast magnetosonic point is analyzed in detail under the assumption of magnetically dominated limit. It is found that this condition restricts the shape of the magnetic field lines threading the event horizon. For example, cylindrical field lines must be sent into radial or paraboloidal ones. The plasma is expected to be injected from a thin disk into the magnetosphere and accretes to the event horizon. We calculate the fluid's energy and angular momentum both at the injection region and at the event horizon to investigate their MHD transport along the field lines. It is clearly shown that the fluid's energy and angular momentum at the event horizon do not depend so much on the initial conditions at the injection region, but rather vary with the field line geometry near the event horizon. Therefore, we conclude that the transport process between the fluid and the magnetic field should be sufficiently effective in the accretion. Interestingly, the fluid's energy can become negative at the event horizon even if it is positive at the injection region. This is a Penrose mechanism due to the MHD energy extraction from the field to the magnetic field.