Spherical trapped-surface conjecture for charged gravitational collapse

Let $\mathcal{Q}^+$ be the quotient of the maximal future development, $J^-(\mathcal{I}^+)$ the causal past of future null infinity, $\mathcal{A}$ the apparent horizon, and $b_{\Gamma}$ the relevant endpoint on the center. Spherical trapped-surface conjecture. Among admissible one-ended data, there exists a generic subclass such that, if

$$\mathcal{Q}^+\cap J^-(\mathcal{I}^+)\neq\emptyset,$$

then $\mathcal{A}$ has a limit point on $b_{\Gamma}$; in that case,

$$\mathcal{S}_{\Gamma}^{1}=\mathcal{CH}_{\Gamma}=\mathcal{S}_{\Gamma}^{2}=\emptyset.$$

This is presented as a charged analogue of Christodoulou’s trapped-surface result and as a statement implying Weak Cosmic Censorship; it remains open in the general charged setting.