2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200570In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture on the physical implications of this characterization for the non linear stability problem for black holes.8 pages, Honorable Mention in the Gravity Research Foundation Essay Competition 2007General Relativity and Quantum Cosmologytext