Limit shocks of relativistic magnetohydrodynamics , Punsly ’ s waveguide and the Blandford - Znajek solution

In this paper we show that switch-on and switch-off shocks are allowed by the shock equations of relativistic MHD and have similar properties to their Newtonian counterparts. Just like in Newtonian MHD they are limits of of fast and slow shock solutions and as such they may be classified as evolutionary shocks. The analysis of Punsly's MHD waveguide problem shows that both fast and Alfvén waves are essential for establishing the global current system in this configuration because Alfvén waves alone cannot switch-on the azimuthal component of magnetic field in the guide. Assuming that this is true in general and using causality argument we conclude that the driving " force " of the Blandford-Znajek mechanism is the black hole ergosphere.