Nonlinear stability of slowly rotating Kerr black holes

Abstract: The issue of the stability of the Kerr family $\KK(a,m)$ has been at the center of attention of GR physics and mathematical relativity ever since their discovery by R.Kerr in 1963.  Roughly the problem here is to show that all spacetime developments of initial data sets, sufficiently close to  that of a Kerr spacetime $\KK(a,m)$ with $|a|/m<1$ , behave asymptotically like a nearby Kerr solution with nearby final parameters $(a_f, m_f)$.  I will talk about recent results which settle the conjecture for the case when $|a|/m$ is sufficiently small.