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

In this essay I first discuss the physical relevance of the inequality m >= root vertical bar J vertical bar for axially symmetric (nonstationary) black holes, where m is the mass and J the angular momentum of the space-time. 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 about the physical implications of this characterization for the nonlinear stability problem for black holes.