A naturalness argument for covered and naked singularities in gravitational collapse

We give a naturalness argument to show that both covered and naked singularities should occur generically in spherical gravitational collapse in classical general relativity, subject to the assumption of the dominant energy condition. An outstanding open problem in classical general relativity and relativistic astrophysics is to determine the final fate of the continual gravitational collapse of a star. The singularity theorems show that, given a few physically reasonable assumptions, such a collapse will terminate in a gravitational singularity. However, the theorems do not by themselves imply that the star ultimately becomes a black hole. In order for a black hole to form, the singularity must be invisible to far away observers. The theorems however allow for the possibility that the singularity may be naked, i.e. visible to a far away observer. Naked singularities, if they were to form in gravitational collapse, are expected to have theoretical and observational properties very different from those of black holes. Because of the difficulty in obtaining a general solution of Einstein equations, it is not known whether classical general relativity generically admits the formation of naked singularities in gravitational collapse [1]. Over the years, various examples of the formation of covered (i.e. not naked) and naked singularities have been found in general relativity, largely in studies of spherical gravitational collapse. Typically, it has been observed that for any given equation of state, both naked and covered singularities arise in these examples, depending on the choice of the initial density and velocity distribution of the star. While on the one hand there is a similarity amongst