Prove generic naked singularity formation from five-dimensional black string instability
In plain words
In five spacetime dimensions a long thin black hole shaped like a string breaks into a chain of smaller black holes, much as a stream of water breaks into drops. Simulations show the pinch-off exposes a singularity to distant observers without fine tuning, but there is no proof.
Precise statement
For the vacuum Einstein equations on asymptotically $R^{3,1} x S^1$ with data near a uniform black string above the Gregory-Laflamme threshold (the length above which the string is unstable), numerical evolution shows a self-similar cascade of thinning necks reaching zero radius in finite asymptotic time (Lehner and Pretorius 2010); thin black rings in asymptotically flat 5D behave similarly (Figueras, Kunesch, Tunyasuvunakool 2016). Prove that an open set of such data yields a maximal development with incomplete future null infinity, a generic violation of weak cosmic censorship in $D = 5$, or prove that the cascade halts.
What would settle it
A rigorous analysis of the nonlinear Gregory-Laflamme evolution establishing or excluding finite-time pinch-off for an open set of data.
Status in the literature
Unverified note
Numerical evidence (2010, 2016) supports finite-time pinch-off in pure gravity; simulations with a positive Gauss-Bonnet correction find curvature growth bounded within effective-field-theory limits (Figueras, Kovacs, Yao, arXiv:2606.05319, 2026); no rigorous proof as of 2026.