Structure of Relativistic Stars Composed of Incompressible Matter in the Absence of Strict Electroneutrality

TL;DR

This paper investigates the structure of relativistic stars made of incompressible, non-electroneutral matter, revealing that non-electroneutrality effects influence chemical potentials even at leading order, with analytical solutions provided.

Contribution

It presents the first analytical solutions for relativistic star models with non-electroneutral incompressible matter, highlighting the significance of non-electroneutrality effects.

Findings

Non-electroneutrality affects chemical potentials at zeroth order.

Analytical solutions for star parameters are derived.

Numerical examples illustrate the theoretical results.

Abstract

The structure of a star composed of locally non-electroneutral incompressible three-component matter is considered within the framework of general relativity. For thermodynamic quantities like the pressure, the solution can be represented as a series in the small parameter $1/\Lambda_{\mathrm G}\sim 10^{-36}$, where the first approximation is the well-known electroneutral solution. However, the equilibrium equations for the chemical potentials of the matter components, as it turns out, contain finite contributions from non-electroneutrality effects even in the zeroth order. Analytical solutions have been obtained for all of the parameters of the problem under consideration, which are illustrated by numerical examples.