Reissner-Nordstrom and charged gas spheres

TL;DR

This paper proposes a variational approach to modeling charged gas spheres, extending the theory of stellar structure to include electromagnetic effects and charged plasmas, with insights into the Reissner-Nordstrom solution.

Contribution

It introduces a variational principle-based model for charged gas spheres, incorporating electromagnetic effects and a novel boundary definition based on the polytropic index change.

Findings

Charged homogeneous models analyzed with gravity and electromagnetism.

Insights into the Reissner-Nordstrom solution in the context of stellar models.

Framework for including radiation effects in future models.

Abstract

The main point of this paper is a suggestion about the proper treatment of the photon gas in a theory of stellar structure and other plasmas. This problem arises in the study of polytropic gas spheres, where we have already introduced some innovations. The main idea, already advanced in the contextof neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is to let mass distribution extend to infinity, the boundary between bulk and atmosphere being defined by an abrupt change in the polytropic index, triggered by the density. The logical next step in this program is to include the effect of radiation, which is a very significant complication since a full treatment would have to include an account of ionization, thus fieldsrepresenting electrons, ions, photons, gravitons and neutral atoms as well. In way of preparation, we consider models that are charged but homogeneous, involving only gravity, electromagnetism and a single scalar field that represents both the mass and the electric charge; in short, anon-neutral plasma. While this work only represents a stage in the development of a theory of stars, without direct application to physical systems, it does shed some light on the meaning of the Reissner-Nordstrom solution of the modified Einstein-Maxwell equations., with an application to a simple system.