Curvature conditions for the occurrence of a class of spacetime singularities

It has recently been shown [W. Rudnicki, Phys. Lett. A 224, 45-50 (1996)] t hat a generic gravitational collapse cannot result in a naked singularity a ccompanied by closed timelike curves. An important role in this result play s the so-called inextendibility condition, which is required to hold for ce rtain incomplete null geodesics. In this paper, a theorem is proved that es tablishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This the orem shows that the inextendibility condition may hold for a much more gene ral class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for st rong curvature singularities can be extended to singularities corresponding to the inextendibility condition. (C) 1999 American Institute of Physics. [S0022-2488(99)02106-4].