2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34142The linear approximation of scalar-tensor theories of gravity is obtained in the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then the weak-field limit is analyzed and the conditions leading to significant deviations of the $1/r^{2}$ Newton's law of gravitation are discussed. Finally, the scalarization effects induced by these theories in extended objects are confronted within the weak-field limit.12 pages in revtex4-twocolumn format; submitted to Phys.Rev.DGeneral Relativity and Quantum Cosmologytext