Uniqueness conjecture for the Kerr family

A Kerr spacetime $(\mathcal{M},g_{a,M})$ is a solution of the Einstein vacuum equations

$$\operatorname{Ric}(g)=0.$$

A solution is called asymptotically flat and stationary if it has the corresponding asymptotic and time-translation properties, and its boundary is a non-degenerate event horizon. An isometry is a distance-preserving diffeomorphism between Lorentzian manifolds.

Uniqueness of the Kerr family. Any sufficiently regular, asymptotically flat, and stationary solution to $\operatorname{Ric}(g)=0$ which is bounded by a non-degenerate event horizon is isometric to a Kerr exterior spacetime.

This conjecture concerns the uniqueness of the possible stationary end states of gravitational collapse. It is presented in the source as one of the fundamental open problems in classical general relativity; the supplied material gives no evidence that the full statement has been resolved.