Towards the proof of the cosmic censorship hypothesis

An attempt is made to formulate the cosmic censorship hypotheses put forward by Penrose (1979) as a theorem which could be subject to a mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity is violated in such a way that causal simplicity also does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis.