Prove weak cosmic censorship for generic 4D vacuum gravitational collapse
In plain words
Weak cosmic censorship says that collapsing matter or gravitational waves never produce a singularity visible from far away, except in finely tuned cases. It has been proved only under strong symmetry assumptions.
Precise statement
For generic asymptotically flat initial data for the 3+1 vacuum Einstein equations (or Einstein equations with physically reasonable matter), prove that the maximal globally hyperbolic development has a complete future null infinity. An answer is a proof, or a counterexample that persists under an open set of perturbations of the data.
What would settle it
A proof of completeness of future null infinity for generic asymptotically flat vacuum data, or a stable counterexample.
Status in the literature
Unverified note
Proved for spherically symmetric Einstein-scalar collapse (Christodoulou 1999); non-generic naked singularities exist for vacuum (Rodnianski and Shlapentokh-Rothman 2019); the generic 4D vacuum case is open as of 2026.