Global geometry of space-time with the charged shell
  It is elaborated the complete classification of the possible types of the spherically symmetric global geometries for two types of electrically charged shells: (1) The charged shell as a single source of the gravitational field, when internal space-time is flat, and external space-time is the Reissner--Nordstr\"om metric; (2) The neutralizing shell with an electric charge opposite to the charge of the internal source with the Reissner--Nordstr\"om metric and with the Schwarzschild metric outside the shell. 
V. A. Berezin and V. I. Dokuchaev
gr-qc