2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201543We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.17 pages, final version, to appear in International Journal of MathematicsDifferential GeometryGeneral Relativity and Quantum Cosmologytext