Stationary equatorial MHD flows in general relativity

We derive a new formulation of the fully general relativistic equations describing a stationary equatorial MHD outflow from a rotating central object. The wind solution appears as a level contour of a "Bernoulli" function fixed by the requirements that it must pass through the slow and fast critical points. This approach is the general relativistic extension to the classical treatment of Sakurai (1985). We discuss in details how the efficiency of the magnetic to kinetic energy conversion depends mainly on the geometry of the flux tubes and show that the magnetic acceleration can work very well under some conditions. We show how this tool can be used for the study of several astrophysical phenomena, among which gamma-ray bursts.