Abstract
Abstract: In this talk I will discuss the physical relevance of the inequality J < m^2, where m and J are the total mass and angular momentum, for axially symmetric (non-stationary) black holes. In particular I will show that for any vacuum, maximal, complete, asymptotically flat, axisymmetric initial data close to extreme Kerr data, this inequality is satisfied. The proof consists in showing that extreme Kerr is a local minimum of the mass.