Slowly rotating charged fluid balls and their matching to an exterior domain

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordström space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by García. The García solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter C₂, characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant C₂ for the García solution. We conjecture that the García metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.