The Klein first integrals in an equilibrium system with electromagnetic, weak, strong and gravitational interactions

TL;DR

This paper generalizes the Klein first integrals to a multi-interaction quantum fermion fluid, including electromagnetic, weak, strong, and gravitational forces, advancing the modeling of neutron star matter.

Contribution

It extends the Klein potentials and related equations to incorporate all fundamental interactions in a relativistic framework for neutron star modeling.

Findings

Generalized Klein potentials for multiple interactions.

Presented a comprehensive set of Einstein-Maxwell-Thomas-Fermi equations.

Facilitates self-consistent relativistic field theoretical modeling of neutron stars.

Abstract

The isothermal Tolman condition and the constancy of the Klein potentials originally expressed for the sole gravitational interaction in a single fluid are here generalized to the case of a three quantum fermion fluid duly taking into account the strong, electromagnetic, weak and gravitational interactions. The set of constitutive equations including the Einstein-Maxwell-Thomas-Fermi equations as well as the ones corresponding to the strong interaction description are here presented in the most general relativistic isothermal case. This treatment represents an essential step to correctly formulate a self-consistent relativistic field theoretical approach of neutron stars.