Cosmic Censorship: Formation of a Shielding Horizon Around a Fragile Horizon

Abstract

The weak cosmic censorship conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside of black holes, invisible to distant observers. This conjecture, put forward by Penrose more than four decades ago, is widely believed to be one of the basic principles of nature. However, a complete proof of this hypothesis is still lacking and the validity of the conjecture has therefore remained one of the most important open questions in general relativity. In this study we analyze a gedanken experiment which is designed to challenge cosmic censorship by trying to overcharge a Reissner-Nordstr\"om black hole: a charged shell is lowered {\it adiabatically} into the charged black hole. The mass-energy delivered to the black hole can be red-shifted by letting the dropping point of the shell approach the black-hole horizon. On the other hand, the electric charge of the shell is not red-shifted by the gravitational field of the black hole. It therefore seems, at first sight, that the charged shell is not hindered from entering the black hole, overcharging it and removing its horizon. However, in the present study we prove that the exposure of a naked singularity to distant observers is actually excluded due to the formation of a new (and {\it larger}) horizon around the original black hole. Moreover, we shall prove that this new horizon is already formed {\it before} the charged shell crosses the original black-hole horizon. This result, which seems to have been previously overlooked, guarantees the validity of the weak cosmic censorship conjecture in this type of gedanken experiments.