Neutral perfect fluids and charged thin shells with electromagnetic mass in general relativity

Abstract

We build extended sources for the Reissner-Nordström metric. Our models describe a neutral perfect fluid core bounded by a charged thin shell, and feature everywhere positive rest mass density and everywhere non-negative active gravitational mass, as well as classical electron radius and electromagnetic total mass. We contrast our results with previously discussed charged anisotropic fluid models which excluded the thin shell and presented similar properties. Our charged thin shells are restricted by the 2D texture equation of state which causes the continuity of the active gravitational mass, in spite of the singularity of the energy-momentum tensor. We mention possible extensions of this study suggested by modified active mass formulae proposed in the literature.