SPHERICALLY SYMMETRICAL SINGULARITIES AND STRONG COSMIC CENSORSHIP

In this paper we consider spherically symmetric metrics having singularities of a form designated as being ''of the power-law type.'' Included in this class are all Tolman-Bondi dust collapses, but the form postulated is very much more general. We calculate the asymptotic behavior of the energy-stress tensor near the singularity, and show that it is possible to satisfy the dominant energy condition, even when the singularity is locally naked. This seems to contradict the strong cosmic censorship hypothesis. However it is shown that if the singularity is not a shell cross, then the energy-stress tensor is asymptotically extreme (\P(r)\ almost-equal-to rho or \P(perpendicular-to)\ almost-equal-to rho) or one of the pressures is negative (P(r) < 0 or P(perpendicular-to) < 0).