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A new code for computing fully general relativistic solutions of stronglymagnetized rapidly rotating compact stars is developed as a part of the COCAL(Compact Object CALculator) code. The full set of Einstein's equations,Maxwell's equations and magnetohydrodynamic equations are consistently solvedassuming perfect conductivity, stationarity, and axisymmetry, and stronglymagnetized solutions associated with mixed poloidal and toroidal components ofmagnetic fields are successfully obtained in generic (non-circular) spacetimes.We introduce the formulation of the problem and the numerical method in detail,then present examples of extremely magnetized compact star solutions and theirconvergence tests. It is found that, in extremely magnetized stars, the stellarmatter can be expelled from the region of strongest toroidal fields. Hence weconjecture that a toroidal electro-vacuum region may appear inside of theextremely magnetized compact stars, which may seem like the neutron starbecoming the strongest toroidal solenoid coil in the universe.

physical review. d/physical review. d.

New code for equilibriums and quasiequilibrium initial data of compact  objects. IV. Rotating relativistic stars with mixed poloidal and toroidal  magnetic fields