2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101328This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: if the energy-momentum is degenerate (in a certain sense) then our 3-manifold can be isometrically embedded in anti de Sitter.2005, 35 pages, to appear in Annales Henri PoincaréDifferential Geometrytext