Global existence conjecture for vacuum Einstein equations with a spacelike translational Killing field

Let $(\Sigma,q,K)$ be asymptotically flat Cauchy data for the $3+1$-dimensional vacuum Einstein equations admitting a spacelike translational Killing field, and let its maximal Cauchy development be the corresponding maximal globally hyperbolic solution. Global existence conjecture. Maximal Cauchy developments of asymptotically flat solutions to the $3+1$ vacuum Einstein equations with a spacelike translational Killing field are regular and geodesically complete. This is an intermediate goal toward the general Cosmic Censorship conjectures for large-data solutions of the Einstein equations. The claim remains open in this setting, although global regularity and cosmic censorship are known in certain more symmetric cases.