Theory of axisymmetric magneto-hydrodynamic flows

A derivation from the weak-gravity limit of general relativity is given of the basic equation for the flux function psi(r,z) for general, steady, axisymmetric, relativistic, ideal magneto-hydrodynamic flows aroud a black hole or a rotating magnetized star. One limit of this equation gives the Grad-Shafranov equation, which describes the equilibrium of axisymmetric fusion plasmas. Another limit gives, except for an additional term, the 'pulsar equation' of Scharlemann, Wagoner, and Michel for relativistic plasma flows around an aligned, rotating, magnetized neutron star