Electrically non-neutral ground states of stars

TL;DR

This paper presents an exact solution to a generalized model of electrically non-neutral stars, revealing bounds on excess charge and supporting cosmic censorship hypotheses, with implications for astrophysics and black hole physics.

Contribution

It provides a complete elementary-function solution to a generalized, exactly solvable model of non-neutral stars, extending previous work to multi-fluid settings and analyzing charge bounds.

Findings

Existence of maximum positive and negative charge solutions for given nuclei

The model captures qualitative behavior of more physical star models

Charge bounds are consistent with black hole charge limits

Abstract

To approximately compute the non-relativistic ground state of an electrically non-neutral star, an exactly solvable model was recently introduced, and partly solved, by Krivoruchenko, Nadyozhin, and Yudin. The model generalizes the well-known Lane--Emden equation of a polytropic gas ball of index $n=1$ to a two-fluid setting. Here its complete solution is presented in terms of simple elementary functions; it is also generalized to a more-than-two-fluid setting where it remains exactly solvable. It is shown that, given the number of nuclei, a maximal negatively and a maximal positively charged solution exists, plus a continuous family of solutions which interpolates between these extremes. Numerical comparisons show that this exactly solvable model captures the qualitative behavior of the more physical model it is supposed to approximate. Furthermore, it correctly answers the question: how non-neutral can the star be? The answer is independent of the speed of light $c$ and the Planck quantum $h$. It supports Penrose's weak cosmic censorship hypothesis, in the sense that the bounds on the excess charge are compatible with the bound on the charge of a Reissner--Weyl--Nordstr\"om black hole.