Dynamical formation and evolution of (2+1)-dimensional charged black holes

Abstract

In this paper, we investigate the dynamical formation and evolution of (2 + 1)-dimensional charged black holes. We numerically study dynamical collapses of charged matter fields in an anti-de Sitter background and note the formation of black holes using the double-null formalism. Moreover, we include renormalized energy-momentum tensors assuming the S-wave approximation to determine thermodynamical back-reactions to the internal structures. If there are no semi-classical effects, the amount of charge determines the causal structures. If the charge is sufficiently small, the causal structure has a space-like singularity. However, as the charge increases, an inner Cauchy horizon appears. If we have sufficient charge, we see a space-like outer horizon and a time-like inner horizon, and if we give excessive charge, black hole horizons disappear. We have some circumstantial evidence that weak cosmic censorship is still satisfied, even for such excessive charge cases. Also, we confirm that there is mass inflation along the inner horizon, although the properties are quite different from those of four-dimensional cases. Semi-classical back-reactions will not affect the outer horizon, but they will affect the inner horizon. Near the center, there is a place where negative energy is concentrated. Thus, charged black holes in three dimensions have two types of curvature singularities in general: via mass inflation and via a concentration of negative energy. Finally, we classify possible causal structures.