Revisiting Relativistic Electrically Charged Polytropic Spheres

Abstract

The problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations is revisited, where the matter model is a polytropic gas. A relativistic polytrope equation of state (EOS) is considered and the electric charge density is assumed to be proportional to the rest mass density. Families of solutions corresponding to various sets of parameters are constructed and analyzed their stability and compliance with the causality requirement, emphasizing the possibility of obtaining black hole mimickers. Concretely, this study wants to test how much electric charge a given object can hold and how compact it can be. It is concluded that there is a microscopic bound on the charge density to rest mass density ratio coincident with the macroscopic bound regarding the extremal Reissner-Nordström (ERN) black hole. The macroscopic charge to mass ratio for the object can exceed the corresponding microscopic ratio if the object is non-extremal. Crucially, the only way to construct a black hole mimicker is by taking a subtle limit in which an electrically counterpoised dust (ECD) solution is attained.