2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33998Global harmonic coordinates for the complete Schwarzschild metric are found for a more general case than that addressed in a previous work by Quan-Hui Liu. The supplementary constant that appears, in addition to the mass, is related to the stress quadrupole moment of a singular energy--momentum tensor. Similar calculations are also carried out in q--harmonic coordinates.20 pages, Plain TeX. Corrected typos and one equation. Conclusions section has been includedGeneral Relativity and Quantum Cosmologytext