ADDENDUM: Rotating Einstein - Maxwell fields: a spacetime with closed timelike lines

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In a recent paper we obtained exact exterior and matching interior stationary axially symmetric solutions of the Einstein - Maxwell field equations for a rigidly rotating charged dust with vanishing Lorentz force. The solutions were expressed in terms of only one of the zeros of the Bessel function 0264-9381/13/4/018/img1. The main aims of this work are to base the exterior and interior solutions on all the infinite number of zeros of 0264-9381/13/4/018/img1, prove the non-existence of timelike hypersurface-orthogonal Killing vectors and that, under a certain condition, the electrovacuum exteriors contain regions with closed timelike lines.

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