Central singularity of the BTZ geometries

Abstract

The nature of the central singularity of the BTZ geometries - stationary vacuum solutions of 2+1 gravity with negative cosmological constant Λ=-ℓ-2 and SO(2)×R isometry - is discussed. The essential tool for this analysis is the holonomy operator on a closed path (i.e., Wilson loop) around the central singularity. The study considers the holonomies for the Lorentz and AdS3 connections. The analysis is carried out for all values of the mass M and angular momentum J, namely, for black holes (Mℓ≥|J|) and naked singularities (Mℓ