Magnetohydrodynamic Shock Conditions for Accreting Plasma onto Kerr Black Holes. I.

Abstract

We extend the work by Appl and Camenzind for special relativistic magnetohydrodynamic (MHD) jets to fully general relativistic studies of standing shock formation for accreting MHD plasma in a rotating, stationary, and axisymmetric black hole magnetosphere. All the postshock physical quantities are expressed in terms of the relativistic compression ratio, which can be obtained in terms of preshock quantities. Then, the downstream state of a shocked plasma is determined by the upstream state of the accreting plasma. In this paper sample solutions are presented for slow magnetosonic shocks for accreting flows in the equatorial plane. We find that some properties of the slow magnetosonic shock for the rotating magnetosphere can behave like a fast magnetosonic shock. In fact, it is confirmed that in the limit of weak gravity for the upstream nonrotating accretion plasma where the magnetic field lines are leading and rotating, our results are very similar to the fast magnetosonic shock solution by Appl and Camenzind. However, we find that the situation becomes far more complicated because of the effects of strong gravity and rotation, such as the frame-dragging effects. We show the tendency that the large spin of the black hole makes the slow magnetosonic shock strong for the accretion solutions with the same energy flux.