Einstein cluster of charged particles

It is shown that there cannot be a spherically symmetric cluster of charged particles in stationary equilibrium having the total amount of charge greater than or equal to the total mass. The result has been proved from the regularity conditions in the interior and the conditions of fit at the boundary with the exterior Reissner-Nordstroem metric. Further a reasonable model is given for a cluster of charged particles representing a conformally flat space-time. (author)