Spherical Gravitating Condensers in General Relativity

TL;DR

This paper investigates spherical charged shell systems in general relativity, analyzing their configurations, energy conditions, and special cases, including exotic scenarios with horizons and curved spacetimes, using Israel's formalism.

Contribution

It provides a detailed analysis of spherical gravitating condensers with charged shells, including general N-shell systems and specific two-shell cases, considering various physical and exotic configurations.

Findings

Classified physically interesting configurations of charged shells.

Identified conditions under which shells can exist below horizons.

Explored scenarios with spacetime curvature confined inside the condenser.

Abstract

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-Nordstr\"om geometry or the spacetime is curved only inside the condenser are considered. Classical limits are mentioned.