Global weak cosmic censorship conjecture

Let $(M,g)$ be a generic, maximal, physically admissible spacetime admitting a complete spacelike hypersurface $\Sigma$. Let $D^+(\Sigma)$ denote its future domain of dependence, let $\mathscr{U}$ be the collection of singular neighborhoods, and let $\mathscr{B}$ be the black region. Global weak cosmic censorship conjecture. There exists a singular neighborhood $U\in\mathscr{U}$ such that

$$U\cap D^+(\Sigma)\subset\mathscr{B}.$$

This is proposed as a global formulation of weak cosmic censorship that does not depend critically on a particular choice of matter fields or on asymptotic flatness. The source describes it as broad and does not provide a resolution.