Extremely charged static dust distributions in general relativity

Conformo static charged dust distributions are investigated in the framework of general relativity. Einstein’s equations reduce to a non-linear version of Poisson’s equation and Maxwell’s equations imply the equality of the charge and mass densities. An interior solution to the extreme Reissner-Nordström metric is given. Dust distributions con-centrated on regular surfaces are discussed and a complete solution is given for a spherical thin shell.