On the equilibrium of self-gravitating neutrons, protons and electrons in \beta-equilibrium

TL;DR

This paper derives and analyzes new equilibrium equations for self-gravitating neutron, proton, and electron systems in e9-equilibrium, challenging traditional models by incorporating charge neutrality violations, finite temperatures, and relativistic effects.

Contribution

It introduces a new set of equilibrium equations that extend the Tolman-Oppenheimer-Volkoff framework to include charge non-neutrality and temperature effects in e9-equilibrium.

Findings

Impossibility of local charge neutrality in e9-equilibrium systems.

Derivation of Newtonian limit of the new equilibrium equations.

Demonstration of the constancy of Klein potentials at finite temperatures.

Abstract

We have recently proved the impossibility of imposing the condition of local charge neutrality in a self-gravitating system of degenerate neutrons, protons and electrons in $\beta$-equilibrium. The coupled system of the general relativistic Thomas-Fermi equations and the Einstein-Maxwell equations have been shown to supersede the traditional Tolman-Oppenheimer-Volkoff equations. Here we present the Newtonian limit of the new equilibrium equations. We also extend the treatment to the case of finite temperatures and finally we give the explicit demonstration of the constancy of the Klein potentials in the case of finite temperatures generalizing the condition of constancy of the general relativistic Fermi energies in the case of zero temperatures.