  We present the self-consistent treatment of the simplest, nontrivial,
self-gravitating system of degenerate neutrons, protons and electrons in
$\beta$-equilibrium within relativistic quantum statistics and the
Einstein-Maxwell equations. The impossibility of imposing the condition of
local charge neutrality on such systems is proved, consequently overcoming the
traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role
of imposing the constancy of the generalized Fermi energies. A new approach
based on the coupled system of the general relativistic
Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an
explicit solution fulfilling global and not local charge neutrality by solving
a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi
equation. The value of the Coulomb potential at the center of the configuration
is $eV(0)\simeq m_\pi c^2$ and the system is intrinsically stable against
Coulomb repulsion in the proton component. This approach is necessary, but not
sufficient, when strong interactions are introduced.
