Cosmic censorship conjecture in some matching spherical collapsing metrics

Abstract

A physically plausible Lema{\^{\i}}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that its {\em intrinsic} energy is, as due, stationary and finite. It is proved for this Lema{\^{\i}}tre-Tolman-Bondi collapse, for some parameter values, that its intrinsic central singularity is globally naked, thus violating the cosmic censorship conjecture with, for each direction, one photon, or perhaps a pencil of photons, leaving the singularity and reaching the null infinity. Our result is discussed in relation to some other cases in the current literature on the subject in which some of the central singularities are globally naked too.