We formulate the set of self-consistent ground-state equilibrium equations for neutron star cores taking into account quantum statistics, electro-weak, and strong interactions, within the framework of general relativity. The strong interaction between nucleons is modeled through the sigmaomega-rho meson exchange in the context of the extended Walecka model, all duly expressed in general relativity. We found the generalization to the works of Klein (1949), of Kodama and Yamada (1972) , and of

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... on and Baylin (1975) by demonstrating that the thermodynamic equilibrium condition of the constancy of the Fermi energy of each particle-specie can be properly generalized to include the contribution of all fields. The consequences of these new conditions of equilibrium on the structure of neutron stars are discussed.