Spherically symmetric charged dust distributions in general relativity

A discussion of the dynamics of charged dust distributions with spherical symmetry is presented. The general behavior is quite complicated and while for rho / /sigma/ a constant greater than unity there is a collapse of the spatial volume, the circumferential area may show an oscillatory behavior (rho and sigma indicate the matter and charge densities respectively). Again for rho / /sigma/ a constant less than unity, the spatial volume would not in general collapse but the circumferential area may do so. However there cannot be any regular oscillation if rho/sigma be constant. Some static and nonstatic solutions are displayed but excepting a class of static solutions, all these have a singularity at the center of symmetry. A static solution, fitted on one side with a Schwarzschild field and on the other side with the Reissner-Nordstrom metric, shows that a star may have around it a shell of charged dust in equilibrium and the charge mass ratio may have arbitrarily large values for the shell