Algebraic classification of 2+1 geometries

Abstract

We present a new effective method of algebraic classification of 2+1 geometries. Our approach simply classifies spacetimes using five real scalars, defined as specific projections of the Cotton tensor onto a suitable null basis. The algebraic type of a spacetime is determined by gradual vanishing of these scalars. We derive the Bel-Debever criteria, together with the multiplicity of the Cotton aligned null directions (CANDs). Additionally, we provide a frame-independent algorithm for classification based on the polynomial curvature invariants and show the equivalence to previous methods of classification.