Cosmic Censorship Conjecture violation: A semiclassical approach

Abstract: The Cosmic Censorship Conjecture (CCC) states that every singularity (except the cosmological one) must appear "dressed" in the universe. This statement was introduced by Roger Penrose (Penrose, 1969), meaning that every singularity (except the Big Bang) in the universe must be hidden inside an Event Horizon. Mathematically, this is described by the inequality $M^2 \geqslant Q^2 + a^2$ (in geometrized unit system), with $M$ being the mass of the black hole, $Q$ its charge and $a := J/M$ its specific angular momentum. Essentially, this three quantities determines uniquely a black hole, as stated by the no-hair theorem. We study the emission probability of a massive ($m_w$) uncharged scalar wave packet, a semi-classical approximation for a particle, by a static, charged black hole. We show that for a few values of the mass $\mathcal{M} := M+\delta M$ (where $M$ is the fixed value for the mass and $\delta M$ being a small variation to $M$ in the order of $m_w$) with different values for $\delta M$ and fixed charge $Q$ for the black hole, the emission probability tends to zero once the Cosmic Censorship Conjecture is close to be violated, that is, when the emitted packet is such that the new quantity $\mathcal{M}' := \mathcal{M}-m_w$ would violate the inequality $\mathcal{M}' > Q$.