We present the set of equilibrium equations for a self-gravitating system of degenerate neutrons, protons and electrons in beta equilibrium in the framework of relativistic quantum statistics and the Einstein-Maxwell equations. Special emphasis is given to the crucial role of the constancy of the generalized Fermi energy of particles from which we formulate the general relativistic version of the Thomas-Fermi equation. We discuss briefly the consequences of this approach in the general case of neutron star configurations with a core and a crust.