Dimension of the isometry group in type N vacuum solutions: an IDEAL approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917188134240256 |
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| author | Sáez, Juan Antonio Mengual, Salvador Ferrando, Joan Josep |
| author_facet | Sáez, Juan Antonio Mengual, Salvador Ferrando, Joan Josep |
| contents | The necessary and sufficient conditions for a type N vacuum solution (with cosmological constant) to admit a group of isometries of dimension $r$ are given in terms of the invariant concomitants of the Weyl tensor. This study requires defining several invariant classes, and for each class, the conditions that determine the dimension are given. Thus, an IDEAL (Intrinsic, Deductive, Explicit and ALgorithmic) characterisation of these spacetimes follows. Some examples show that our algorithmic results can easily be implemented on the \textit{xAct Mathematica} suite of packages. The relation between our classes and already known families of solutions of Einstein equations is outlined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension of the isometry group in type N vacuum solutions: an IDEAL approach Sáez, Juan Antonio Mengual, Salvador Ferrando, Joan Josep General Relativity and Quantum Cosmology The necessary and sufficient conditions for a type N vacuum solution (with cosmological constant) to admit a group of isometries of dimension $r$ are given in terms of the invariant concomitants of the Weyl tensor. This study requires defining several invariant classes, and for each class, the conditions that determine the dimension are given. Thus, an IDEAL (Intrinsic, Deductive, Explicit and ALgorithmic) characterisation of these spacetimes follows. Some examples show that our algorithmic results can easily be implemented on the \textit{xAct Mathematica} suite of packages. The relation between our classes and already known families of solutions of Einstein equations is outlined. |
| title | Dimension of the isometry group in type N vacuum solutions: an IDEAL approach |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.20427 |