Magnetohydrodynamics of Rotating Black Holes

Abstract

Magnetic fields are important for the physics of accretion disks around black holes, accretion flows should be formulated in terms of magnetohydrodynamics. Such magnetohydrodynamic flows near rapidly rotating compact objects must include the relativistic effects of the underlying metric. Of special importance are supermassive black holes in the centers of galaxies. The evidence for the existence of these objects is shortly discussed. The basic features of resistive magnetohydrodynamics (RMHD) are reviewed for plasma flows on the background of rotating black holes. We give a comprehensive derivation of the basic equations, with particular emphasis on axisymmetric configurations. We derive the relevant time—dependent equations for the poloidal magnetic flux and the poloidal current function for accretion disks around rapidly rotating black holes. In particular, we discuss the role of the gravitomagnetic force for the evolution of magnetic fields around black holes.

Magnetic fields in accretion disks also influence the accretion process onto black holes. These processes are discussed within a stationary approach using infinite conductivity near black holes. The theory of stationary MHD flows on rotating backgrounds is now complete and can be applied to various situations, outflows, and inflows. We discuss in particular magnetic accretion onto a rotating black hole and demonstrate the Blandford—Znajek process; for sufficiently rapidly rotating black holes, the accretion can carry a negative total angular momentum inwards, spinning down in this way the black hole. We also shortly discuss magnetized disk outflows near black holes, as well as the question of magnetic jet collimation.