A Two Species Thomas-Fermi Model for Stellar Ground States

TL;DR

This paper develops a two-fluid Thomas-Fermi model for self-gravitating charged bodies, proving existence, compact support, and uniqueness of minimizers under certain conditions, with extensions to relativistic cases.

Contribution

It introduces a novel two-species Thomas-Fermi energy functional for stellar models, establishing existence, uniqueness, and shape properties of minimizers in both non-relativistic and relativistic regimes.

Findings

Existence of minimizers under specific charge conditions

Minimizers have compact support

Uniqueness of the minimizer in the non-relativistic case

Abstract

We present an energy functional for a Thomas-Fermi type two-fluid model of a self-gravitating non-rotating charged body, with a non-relativistic kinetic energy. We prove that, under certain conditions on the total number of positively charged and negatively charged particles, a minimizer exists and both fluids have compact support. We prove the same result for special relativistic kinetic energy, assuming further conditions on the total number of particles. In the non-relativistic kinetic energy case, we further prove the uniqueness of the minimizer, as well as present results relating the general shape of the minimizer to the total number of particles.