Victor Berezin & Vyacheslav Dokuchaev 
Global Geometry of Space-Times with Shells [PDF ebook] 

In this book, the complete classification of the possible types of spherically symmetric global geometries for two types of electrically charged shells are explored. These include the charged shell as a single source of the gravitational field, when internal space-time is flat, and external space-time is the Reissner–Nordstrom metric; and the neutralizing shell with an electric charge opposite to the charge of the internal source with the Reissner–Nordstrom metric and with the Schwarzschild metric outside the shell. Starting from Israel equations for the spherically symmetric thin shells, this book introduce the effective potential and shows how it can be used in constructing, without further thorough investigation, the corresponding Carter–Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. This book demonstrates how this new method works by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner–Nordstrom electro-vacuum manifolds.