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In 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 themass and J the angular momentum of the spacetime. Then, I present a proof ofthis inequality for the case of one spinning black hole. The proof involves aremarkable characterization of the extreme Kerr black hole as an absoluteminimum of the total mass. Finally, I conjecture on the physical implicationsof this characterization for the non linear stability problem for black holes.

The inequality between mass and angular momentum for axially symmetric black holes