MHD Shock Conditions for Accreting Plasma onto Kerr Black Holes - I
  We extend the work by Appl and Camenzind (1988) for special relativistic magnetohydrodynamic (MHD) jets, to fully general relativistic studies of the 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 non-rotating 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 (1988). However, we find that the situation becomes far more complicated due to 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. 
Masaaki Takahashi, Darrell Rilett, Keigo Fukumura, and Sachiko Tsuruta