Stability of Kerr conjecture

Let $K(a,M)$ be a Kerr spacetime with $0\leq |a|\leq M$, and let vacuum initial data sets be sufficiently close to Kerr initial data. Stability of Kerr conjecture. Their maximal developments have complete future null infinity and a domain of outer communication which approaches, globally, a nearby Kerr solution. This is a central nonlinear stability problem in general relativity. The stability of Kerr has been proved for small angular momentum, $|a|\ll M$, but remains open for general Kerr parameters.