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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2310.10528 |
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| _version_ | 1866916332204720128 |
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| author | Podolsky, Jiri Papajcik, Matus |
| author_facet | Podolsky, Jiri Papajcik, Matus |
| contents | A new effective approach to the algebraic classification of geometries in 2+1 gravity is presented. It uses five real Cotton scalars $Ψ_A$ of distinct boost weights, which are 3D analogues of the Newman-Penrose scalars representing the Weyl tensor in 4D. The classification into types I, II, D, III, N, O is directly related to the multiplicity of the four Cotton-aligned null directions (CANDs). We derive a synoptic algorithm based on the invariants constructed from $Ψ_A$, and we show its agreement with the Petrov scheme based on eigenvalues and canonical Jordan form of the Cotton-York tensor. Our method is simpler and also general because it can be used in any 2+1 theory, such as Einstein's gravity or topologically massive gravity. As an example we analyze the algebraic structure of Robinson-Trautman spacetimes which include charged black holes with a cosmological constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10528 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A novel classification method of 2+1 spacetimes based on the Cotton scalars Podolsky, Jiri Papajcik, Matus General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics A new effective approach to the algebraic classification of geometries in 2+1 gravity is presented. It uses five real Cotton scalars $Ψ_A$ of distinct boost weights, which are 3D analogues of the Newman-Penrose scalars representing the Weyl tensor in 4D. The classification into types I, II, D, III, N, O is directly related to the multiplicity of the four Cotton-aligned null directions (CANDs). We derive a synoptic algorithm based on the invariants constructed from $Ψ_A$, and we show its agreement with the Petrov scheme based on eigenvalues and canonical Jordan form of the Cotton-York tensor. Our method is simpler and also general because it can be used in any 2+1 theory, such as Einstein's gravity or topologically massive gravity. As an example we analyze the algebraic structure of Robinson-Trautman spacetimes which include charged black holes with a cosmological constant. |
| title | A novel classification method of 2+1 spacetimes based on the Cotton scalars |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2310.10528 |