On a lower-dimensional Killing vector origin of irreducible Killing tensors

Article

On a lower-dimensional Killing vector origin of irreducible Killing tensors

Gray, F.; Odak, G.; Krtouš, P.; Kubizňák, D.

J. High Energy Phys. 2507, 098 (2025)

Abstract

Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction, the key ingredient for irreducibility is the non-commutativity of the underlying Killing vectors. It gives rise to a tower of growing rank Killing tensors determined by the structure constants of the corresponding Lie algebra. A canonical example of a metric with such emergent non-trivial hidden symmetries in all dimensions is provided by rotating (off-shell) generalized Lense-Thirring spacetimes, where the irreducible Killing tensors arise from the underlying spherical symmetry of the base space. A physical on-shell realization of this construction in four dimensions is embodied by a rotating black hole in the Einstein-Maxwell-Dilaton-Axion theory. Further examples of equal spinning Myers-Perry spacetimes and spacetimes built on planar and Taub-NUT base metrics are also discussed.

Institute authors

Supported by

GACR 22-14791S — Černoděrové prostoročasy v obecné dimenzi, jejich vlastnosti a interpretace
GACR 23-07457S — Skryté symetrie a chemie černých děr
UNCE24/SCI/016 — Centrum částicové fyziky a kosmologie

BibTeX

@article{UTF1023,
  author        = {Gray, F. and Odak, G. and Krtouš, P. and Kubizňák, D.},
  title         = {{On a lower-dimensional Killing vector origin of irreducible Killing tensors}},
  journal       = {J. High Energy Phys.},
  volume        = {2507},
  pages         = {098},
  year          = {2025},
  doi           = {10.1007/JHEP07(2025)098},
  eprint        = {2504.18287},
  archivePrefix = {arXiv},
}