2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203821Exploiting a 3+1 analysis of the Mars-Simon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of a positive scalar function defined on the initial data hypersurface. Applications of this result are discussed.23 pages, 1 figure. Minor typos corrected and remark 2 added. To appear in Classical and Quantum GravityGeneral Relativity and Quantum Cosmologytext