2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211902We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence, we obtain that any data in this class satisfy the inequality $\sqrt{J} \leq m$, where $m$ and $J$ are the total mass and angular momentum of the spacetime.The statement before Eq. (17) in page 5 in the previous version is incorrect. This mistake is corrected in the new versionGeneral Relativity and Quantum CosmologyMathematical PhysicsDifferential Geometrytext