2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193043The renormalized mean value of the quantum Lagrangian and the corresponding components of the Energy-Momentum tensor for massive spinor fields coupled to an arbitrary gravitational field configuration having cylindrical symmetry are analytically evaluated using the Schwinger-DeWitt approximation, up to second order in the inverse mass value. The general results are employed to explicitly derive compact analytical expressions for the quantum mean Lagrangian and Energy- Momentum tensor in the particular background of the Black-String space-time.15 pages, few corrections are done in this versionGeneral Relativity and Quantum Cosmologytext