A combined rotating charged dust-surface layer source for the McCrea electrovacuum

Abstract

The McCrea electrovacuum is one of the few known stationary cylindrically symmetric solutions of the Einstein-Maxwell field equations. In the purely gravitational case in which the electromagnetic field is absent, a source was obtained in the form of an infinitely long cylindrical shell. In this work, we obtain a source of the complete McCrea electrovacuum, which is also in the form of an infinitely long cylindrical shell, but in this case the shell is the boundary of rotating charged dust. The source of the complete McCrea electrovacuum found here therefore; is a combination of rotating charged dust, bounded by an infinitely long cylindrical shell which is rotating with the dust.