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arXiv · 2504.18287

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

Finnian Gray·Gloria Odak·Pavel Krtouš·David Kubizňák
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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.

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Finnian Gray, Gloria Odak, Pavel Krtouš, David Kubizňák. 2025-04-25. On a lower-dimensional Killing vector origin of irreducible Killing tensors. https://doi.org/10.1007/jhep07(2025)098

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