  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 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.
