Disc sources for conformastationary metrics

Conformastationary metrics - those of the form have been derived by Perjes and by Israel and Wilson as source-free solutions of the Einstein-Maxwell equations. By analogy with the conformastatic metrics which have charged dust sources it was assumed that conformastationary metrics would be the external metrics of charged dust in steady motion. However, for axially symmetric conformastationary metrics we show that, as well as moving dust, hoop tensions are always necessary to balance the centrifugal forces induced by the motion. Exact examples of conformastationary metrics with disc sources are worked out in full. Generalizations to non-axially symmetric conformastationary metrics are indicated.