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arXiv · 2509.22309

Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes

Aimeric Colléaux·Ivan Kolář·Tomáš Málek
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Abstract

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.

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Aimeric Colléaux, Ivan Kolář, Tomáš Málek. 2025-10-03. Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes. https://doi.org/10.1103/y6sl-b6x4

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