Surface-Gravity Inequalities and Generic Conditions for Strong Cosmic Censorship

Abstract

Transforming Penrose's intuitive picture of a strong cosmic censorship principle, that generically forbids the appearance of locally naked space-time singularities, into a formal mathematical proof, remains at present, one of the most outstanding unsolved mathematical problems from the theory of gravitational collapse. Part of the difficulty lies in the fact that we do not possess yet a clear-cut understanding of the hypothesis needed for the establishment of some sort of strong cosmic censorship theorem. What we have is a selected list of solutions, which at first sight seem to go against cosmic censorship, but at the end they fail in some way. However, the space of solutions of Einstein's field equations is vast. In this article, we plan to increase one's intuition by establishing a link between certain inequalities for Cauchy-horizon stability and a set of generic conditions, such as a reasonable equation of state--which determines whether the space-time is asymptotically flat or not, an energy condition, and an hypothesis over the class of metrics on which Einstein's field equations ought to be solved to ensure strong cosmic censorship inside black-holes. With these tools in hand we examine the Cauchy-horizon stability of the theory created by Born and Infeld--whose action principle has been used as a prototype in superstring theory, and the singularity-free Bardeen's black-hole model.