2025/11/10 by Matúš Papajčík, Papajcik, Matus, Jiřı́ Podolský +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2511.07621
openalex publication_date 2025/11/10 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28
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.