New quasi-Einstein metrics on a two-sphere
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917508524539904 |
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| author | Colling, Alex Dunajski, Maciej Kunduri, Hari Lucietti, James |
| author_facet | Colling, Alex Dunajski, Maciej Kunduri, Hari Lucietti, James |
| contents | We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New quasi-Einstein metrics on a two-sphere Colling, Alex Dunajski, Maciej Kunduri, Hari Lucietti, James Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor. |
| title | New quasi-Einstein metrics on a two-sphere |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.04117 |