2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55624We perform a foliation of a four dimensional Riemannian space-time with respect to a discrete time which is an integer multiple of the Planck time. We find that the quantum fluctuations of the metric have a discrete energy spectrum. The metric field is expanded in stationary eigenstates, and this leads to the description of a de Sitter-like universe. At the Planck scale the model describes a Planckian Euclidean black hole.16 pages HTMLHigh Energy Physics - Theorytext