Free Energy of Gravitating Fermions

TL;DR

This paper develops a relativistic Thomas-Fermi model for self-gravitating fermions, linking free energy extremization to Einstein's equations, and deriving self-consistent equations for the system.

Contribution

It introduces a novel general-relativistic Thomas-Fermi framework for analyzing self-gravitating fermion systems, connecting thermodynamic and gravitational equations.

Findings

Derivation of a free energy functional for self-gravitating fermions.

Equivalence between free energy extremization and Einstein's equations.

Formulation of self-consistency equations for the fermion gas.

Abstract

We study a system of self-gravitating massive fermions in the framework of the general-relativistic Thomas-Fermi model. We postulate the free energy functional and show that its extremization is equivalent to solving the Einstein's field equations. A self-gravitating fermion gas we then describe by a set of Thomas-Fermi type self-consistency equations.