Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes
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| Format: | Preprint |
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2025
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| _version_ | 1866908919814684672 |
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| author | Colléaux, Aimeric Kolář, Ivan Málek, Tomáš |
| author_facet | Colléaux, Aimeric Kolář, Ivan Málek, Tomáš |
| contents | We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes, one can obtain symmetries of the near-horizon extreme Kerr (NHEK) geometry or swirling universe by complex analytic continuations of coordinates. Similarly, the static spherical/hyperbolic/planar symmetries (i.e., symmetries of the Schwarzschild spacetime and other A-metrics) are mapped to symmetries of the B-metrics (or Melvin spacetime). All these mappings are theory-independent -- they constitute relations among symmetries themselves, and, hence among the classes of symmetry-invariant metrics and electromagnetic field strengths, rather than among specific solutions. Consequently, finding, e.g., vacuum Taub-NUT-type solutions in a given gravitational theory automatically yields vacuum NHEK- or swirling-type solutions of that theory, with a possible extension to the electromagnetic case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes Colléaux, Aimeric Kolář, Ivan Málek, Tomáš General Relativity and Quantum Cosmology High Energy Physics - Theory We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes, one can obtain symmetries of the near-horizon extreme Kerr (NHEK) geometry or swirling universe by complex analytic continuations of coordinates. Similarly, the static spherical/hyperbolic/planar symmetries (i.e., symmetries of the Schwarzschild spacetime and other A-metrics) are mapped to symmetries of the B-metrics (or Melvin spacetime). All these mappings are theory-independent -- they constitute relations among symmetries themselves, and, hence among the classes of symmetry-invariant metrics and electromagnetic field strengths, rather than among specific solutions. Consequently, finding, e.g., vacuum Taub-NUT-type solutions in a given gravitational theory automatically yields vacuum NHEK- or swirling-type solutions of that theory, with a possible extension to the electromagnetic case. |
| title | Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.22309 |