Relativistic stars with poloidal and toroidal magnetic fields and meridional flow

We investigate stationary axisymmetric configurations of magnetized stars in the framework of general relativistic ideal magnetohydrodynamics. Our relativistic stellar model incorporates a toroidal magnetic field and meridional flow in addition to a poloidal magnetic field for the first time. The magnetic field and meridional flow are treated as perturbations, but no other approximation is made. We find that the stellar shape can be prolate rather than oblate when a toroidal field exists. We also find that, for fixed baryonic mass and total magnetic helicity, more spherical the star is, lower the energy it has. Further, we find two new types of the frame dragging effect which differ from the standard one in a rotating star or Kerr geometry. They may violate the reflection symmetry about the equatorial plane.