On a lower-dimensional Killing vector origin of irreducible Killing tensors
arXiv:2504.18287 · doi:10.1007/JHEP07(2025)098
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.
arXiv commentv3. Section 2 rewritten to correct minor mistake. Results remain unchanged modulo some arising subtleties
References in corpus (34)
- The General Kerr-de Sitter Metrics in All Dimensions
- Rotating Charged Black Hole Solution in Heterotic String Theory
- Rotating Black Holes in Higher Dimensions with a Cosmological Constant
- Black holes, hidden symmetries, and complete integrability
- Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
- Linear dilaton black holes
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- Ehlers--Harrison--Type Transformations in Dilaton--Axion Gravity
- Komar Integrals in Higher (and Lower) Derivative Gravity
- Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
- Killing Initial Data
- A Bestiary of Higher Dimensional Taub-NUT-AdS Spacetimes
- Carrollian and Galilean conformal higher-spin algebras in any dimensions
- NUTs and bolts beyond Lovelock
- Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
- Some Spacetimes with Higher Rank Killing-Stackel Tensors
- Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
- Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces
- Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension
- Conformal Yano-Killing tensors for the Taub-NUT metric
- Killing tensor and Carter constant for Painleve-Gullstrand form of Lense-Thirring spacetime
- Killing tensors and photon surfaces in foliated spacetimes
- Aspects of Holography of Taub-NUT-AdS4
- On integrability of the Killing equation
- KIDs like cones
- Killing-Yano forms and Killing tensors on a warped space
- Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter
- Slowly rotating black holes with exact Killing tensor symmetries
- Love symmetry in higher-dimensional rotating black hole spacetimes
- Symmetry reduction of gravitational Lagrangians
- Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation
- Killing tensors of generalized Lense-Thirring space-time
- Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector