Kerr stability conjecture for subextremal Kerr spacetimes

Let $({\mathcal M},{\textbf{g}})$ be a four-dimensional Lorentzian manifold satisfying the Einstein vacuum equations $\operatorname{Ric}({\textbf{g}})=0$. For parameters $m$ and $a$ with $|a|<m$, let $({\mathcal M},{\textbf{g}}_{a,m})$ be a subextremal Kerr spacetime, and let a subextremal Kerr initial data set mean initial data induced by such a spacetime. The maximal Cauchy development is the maximal spacetime development determined by an initial data set for the Einstein vacuum equations.

Kerr stability conjecture. The maximal Cauchy development of any initial data set for the Einstein vacuum equations, sufficiently close to a subextremal Kerr initial data set in a suitable sense, has a complete future null infinity and a domain of outer communication, which is asymptotic to a nearby member of the subextremal Kerr family.

This is one of the central open problems in general relativity. It asserts the nonlinear stability of subextremal Kerr black holes under sufficiently small perturbations, including completeness of future null infinity and asymptotic convergence of the exterior region to a nearby Kerr spacetime.