Reissner–Nordström and Charged Gas Spheres

Abstract

This paper studies polytropic gas spheres with some innovations. The main idea, already advanced in the context of neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is that the mass distribution extends 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 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 fields representing 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, a non-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–Nordström solution of the modified Einstein–Maxwell equations. But the main point of the paper is a suggestion about the proper place of the photon gas in a theory of stellar structure and other plasmas, with an application to a simple system; it is proposed to treat the photon gas as part of the dynamics.