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

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Main Authors: Colléaux, Aimeric, Kolář, Ivan, Málek, Tomáš
Format: Preprint
Published: 2025
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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
id 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