Rotating charged dust as a source for cylindrically symmetric electrovacs

Abstract

Exact solutions for stationary rotating charged dust with cylindrical symmetry, for which one of the spacelike Killing vectors is hypersurface orthogonal, are considered. The general solution for the case of rigid rotation and constant charge to mass ratio is given. It is proved that all rigidly rotating solutions can be joined smoothly to the exterior electrovac solutions involving third Painlevé transcendents. Also the solutions for differentially rotating charged dust, which have a force-free electromagnetic field can be matched to a particular class of the electrovac metrics.