On a lower-dimensional Killing vector origin of irreducible Killing tensors
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.
Cite
@article{arxiv.2504.18287,
title = {On a lower-dimensional Killing vector origin of irreducible Killing tensors},
author = {Finnian Gray and Gloria Odak and Pavel Krtouš and David Kubizňák},
journal= {arXiv preprint arXiv:2504.18287},
year = {2026}
}
Comments
v3. Section 2 rewritten to correct minor mistake. Results remain unchanged modulo some arising subtleties