Spherical gravitating condensers in general relativity

By a spherical gravitating condenser we mean two concentric charged shells made of perfect fluids restricted by the condition that the electric field is nonvanishing only between the shells. Flat space is assumed inside the inner shell. By using Israel’s formalism we first analyze the general system of $N$ shells and then concentrate on the two-shell condensers. Energy conditions are taken into account; physically interesting cases are summarized in two tables, but also more exotic situations in which, for example, the inner shell may occur below the inner horizon of the corresponding Reissner-Nordström geometry or the spacetime is curved only inside the condenser are considered. Classical limits are mentioned.

Figure 1

A sketch of the sequence of shells: $M_A$, $Q_A$ are the masses and charges in the respective spaces and $R_A$ the radii of the shells. The metric function $f_A$ will only play a role in Sec. 3.