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

TL;DR

This paper constructs models of extended sources for the Reissner-Nordström metric involving a neutral perfect fluid core and a charged thin shell, ensuring positive mass density and gravitational mass, contrasting with previous anisotropic models.

Contribution

It introduces a new class of models with positive mass density and gravitational mass, using a 2D texture equation of state to maintain active mass continuity despite singularities.

Findings

Models have positive rest mass density and non-negative active gravitational mass.

Charged thin shells obey a 2D texture equation of state.

Active gravitational mass remains continuous despite energy-momentum tensor singularities.

Abstract

We build extended sources for the Reissner-Nordstr\"{o}m 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 models featuring similar properties at the expense of including anisotropic pressures within the fluid. 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.