Global geometry of space-time with the charged shell

TL;DR

This paper classifies all possible spherically symmetric global geometries involving charged shells, analyzing configurations with either a single charged shell or a neutralizing shell, and their resulting space-time structures.

Contribution

It provides a complete classification of spherically symmetric space-time geometries involving charged shells, including cases with flat interior and Reissner-Nordström exterior or neutralizing shells.

Findings

Classified possible global geometries for charged shells

Analyzed configurations with flat interior and Reissner-Nordström exterior

Examined neutralizing shells with Reissner-Nordström and Schwarzschild metrics

Abstract

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.