Reissner-Nordstrom and charged gas spheres

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.Comment: 19 pages, plain te

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure