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Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal and toroidal magnetic fields are obtained numerically. Because of the mixed components of the magnetic field, the underlying stationary and axisymmetric spacetimes are no longer circular. These configurations are computed from the full set of the Einstein-Maxwell equations, Maxwell's equations, and from first integrals and integrability conditions of the magnetohydrodynamic equilibrium equations. After a brief introduction of the formulation of the problem, we present the first results for highly deformed magnetized rotating compact stars.
Uryū et al. (Fri,) studied this question.