2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/199375We study our non-perturbative formalism to describe scalar gauge-invariant metric fluctuations by extending the Ponce de Leon metric.accepted in Eur. Phys. J. CGeneral Relativity and Quantum CosmologyNon-perturbative scalar gauge-invariant metric fluctuations from the Ponce de Leon metric in the STM theory of gravitytext