Static distribution of charged dust in general relativity

The paper considers charged dust distributions in equilibrium. If the dust be uniformly charged (i.e. if the ratio of the charge density to the matter density be constant) or if the surfaces of the dust distributions be equipotential surfaces and inside these surfaces there is no hole or pocket of alien matter, then there exists a simple relation between g$_{00}$ and $\phi$, the electrostatic potential and the charge density must be equal to the matter density. Further in this case, the whole system of field equations can be reduced to a single Laplace equation in the empty space outside and to a nonlinear modified Poisson equation within the charged dust distributions.