Algebraic classification of 2+1 geometries
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918194420121600 |
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| author | Papajcik, Matus Podolsky, Jiri |
| author_facet | Papajcik, Matus Podolsky, Jiri |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic classification of 2+1 geometries Papajcik, Matus Podolsky, Jiri General Relativity and Quantum Cosmology 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. |
| title | Algebraic classification of 2+1 geometries |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.07621 |