2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113612We study the gravitational collapse of a dust dark matter star in a $Λ$-background. We consider two distinct cases: First we do not have a dark matter and dark energy coupling; second, we consider that $Λ$ decay in dark particles. The approach adopted assumes a modified matter expansion rate and we have formation of a black hole, since that, we have the formation of an apparent horizon. A brief comparison of the process of the matter condensation using the gravitational collapse approach and the linear scalar perturbation theory is considered.9 pages, 3 figuresGeneral Relativity and Quantum Cosmologytext