The cosmic censorship hypothesis for maximal Cauchy developments

Let $(\Sigma, h_{ab}, k_{ab})$ be an initial data set with $\Sigma$ three-dimensional. A spacetime is strongly causal if every point $p$ and neighborhood $O$ of $p$ have a neighborhood $V\subseteq O$ that no causal curve intersects more than once. For an initial data set, let $H^+(\Sigma)$ denote its future Cauchy horizon and let $I^-(p)$ denote the chronological past of $p$. Cosmic censorship hypothesis. If the maximal Cauchy development of this initial data is extendible, then for each $p\in H^+(\Sigma)$ in any extension, either strong causality is violated at $p$ or

$$\overline{I^-(p)\cap\Sigma}$$

is noncompact. This is a formulation of cosmic censorship intended to exclude physically unreasonable extensions with naked singularities; the source does not establish its resolution.