  For sake of simplicity, concentrate on the initial value problem for  vacuum solutions \((T_{ab} \equiv 0)\) to Einstein’s  field equations. Start with a three-manifold \(\Sigma\) equipped with  quantities which, when \(\Sigma\) is embedded as a spacelike submanifold of spacetime, become initial data for the vacuum field equations.  Corresponding to the initial data there exists a   unique[20]  maximal development   \((\mathcal{M}, g_{ab})\) for which (the image  of the embedded) \(\Sigma\) is a Cauchy   surface.[21]  This solution, however, may not be maximal simpliciter, i.e., it may  be possible to isometrically embed it as a proper part of a larger  spacetime, which itself may be a vacuum solution to the field  equations; if so \(\Sigma\) will not be a Cauchy surface for the  extended spacetime, which fails to be a globally hyperbolic   spacetime.[22]  This situation can arise because of a poor choice of initial value  hypersurface, as illustrated in   Figure 3  by taking \(\Sigma\) to be the indicated spacelike hyperboloid of \((1 +  1)\)-dimensional Minkowski spacetime. But, more interestingly, the  situation can arise because the Einstein equations allow various  pathologies, collectively referred to as “naked  singularities,” to develop from regular initial data. The  strong form of Penrose’s celebrated cosmic censorship  conjecture proposes that, consistent with Einstein’s field  equations, such pathologies do not arise under physically reasonable  conditions or else that the conditions leading to the pathologies are highly non-generic within the space of all solutions to the field  equations. A small amount of progress has been made on stating and  proving precise versions of this   conjecture.[23] 