Rotating charged dust in general relativity

Abstract

Considers a distribution of charged dust in rigid motion where the electromagnetic potential vector Amu =kvmu , vmu being the velocity vector of the dust. Such a relation makes the magnetic field vector everywhere coincident in direction with the vorticity tensor. Without introducing any specific symmetry assumption. Maxwell's equations and some of the Einstein equations yield some constraints on the ratio of charge to mass density. The investigation further leads to some coordinate-independent formulae from which it seems possible to construct hitherto unknown solutions of the Einstein-Maxwell equations for distributions of charged dust for both constant and non-constant k.