Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918388459110400 |
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| author | Sato, Yuichiro Tsuyuki, Takanao |
| author_facet | Sato, Yuichiro Tsuyuki, Takanao |
| contents | When the maximal isometry group of a four-dimensional spacetime acts simply transitively, such a Ricci-flat metric is uniquely determined to be the Petrov solution. This isometry group is almost abelian; that is, its Lie algebra contains an abelian ideal of codimension one. In this paper, we study Lorentzian left-invariant metrics on almost abelian Lie groups of dimension four or higher. In particular, we construct a Ricci-flat but non-flat metric that generalizes the Petrov solution to arbitrarily high dimensions. The generalized solution is geodesically complete and admits closed timelike curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups Sato, Yuichiro Tsuyuki, Takanao Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Primary 53B30, Secondary 53C30 When the maximal isometry group of a four-dimensional spacetime acts simply transitively, such a Ricci-flat metric is uniquely determined to be the Petrov solution. This isometry group is almost abelian; that is, its Lie algebra contains an abelian ideal of codimension one. In this paper, we study Lorentzian left-invariant metrics on almost abelian Lie groups of dimension four or higher. In particular, we construct a Ricci-flat but non-flat metric that generalizes the Petrov solution to arbitrarily high dimensions. The generalized solution is geodesically complete and admits closed timelike curves. |
| title | Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Primary 53B30, Secondary 53C30 |
| url | https://arxiv.org/abs/2504.11077 |