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On rotating charged dust in general relativity

The problem of charged dust rotating about an axis of symmetry is considered both in Newtonian physics and in general relativity. The Newtonian problem is reduced to a single equation in the case of constant rotation, and to two coupled equations in the case of differential rotation, and some explicit cylindrically symmetric solutions are obtained. In general relativity some new cylindrically symmetric exact solutions for constant rotation are derived, and the problem of differential rotation is reduced to four coupled equations for four unknowns.