Cosmic censorship in Lemaitre-Tolman-Bondi spacetimes: Conformal diagrams of locally and globally naked singularities

Abstract

Naked singularities are highly curved regions of spacetime where classical general rel-ativity fails, and whose effects are observable from infinity. The cosmic censorship conjecture states that such singularities must hide behind a black hole event horizon. We consider cosmic censorship in the context of a dust dominated universe, with a spherically symmetric primordial overdensity. This admits an exact description in terms of the Lemaitre-Tolman-Bondi (LTB) solution, in which both black holes and naked singularities can occur. We numerically construct causal diagrams for both cases, identifying the apparent horizons, event horizons and cauchy horizons when applicable