Equilibrium models of relativistic stars with differential rotation and toroidal magnetic fields*

We construct equilibrium models of strongly magnetized neutron stars in general relativity under the assumptions of axisymmetry and stationarity. ~The matter is represented by a magnetized fluid in the ideal MHD approximation and incorporates differential rotation and a toroidal magnetic field. ~We solve for these equilibrium states using a numerical scheme similar to the self-consistent field method. ~We construct as an initial guess a TOV star, add differential rotation and subsequently include the magnetic field. ~ We then explore the parameter space of these equilibrium solutions looking for maximum mass, magnetic field strength, and energy distribution in the star.~