  A formulation is developed for general relativistic ideal
magnetohydrodynamics in stationary axisymmetric spacetimes. We reduce basic
equations to a single second-order partial differential equation, the so-called
Grad-Shafranov (GS) equation. Our formulation is most general in the sense that
it is applicable even when a stationary axisymmetric spacetime is noncircular,
that is, even when it is impossible to foliate a spacetime with two orthogonal
families of two-surfaces. The GS equation for noncircular spacetimes is crucial
for the study of relativistic stars with a toroidal magnetic field or
meridional flow, such as magnetars, since the existence of a toroidal field or
meridional flow violates the circularity of a spacetime. We also derive the
wind equation in noncircular spacetimes, and discuss various limits of the GS
equation.
