Killing tensors and a new geometric duality
arXiv:hep-th/9511166 · doi:10.1016/0550-3213(96)00206-4
Abstract
We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be generalized to spinning spaces, but only at the expense of introducing torsion. This introduces new supersymmetries in their geometry. Interesting examples in four dimensions include the Kerr-Newman metric of spinning black-holes and self-dual Taub-NUT.
20 pages (a4), standard LaTeX, no figures
References in corpus (7)
- SUSY in the sky
- Supersymmetry and the Geometry of Taub-NUT
- New Supersymmetry of the Monopole
- The role of Killing-Yano tensors in supersymmetric mechanics on a curved manifold
- Helicity supersymmetry of dyons
- Generalized Runge-Lenz Vector in Taub-Nut Spinning Space
- The Geodesic Motion in Taub-Nut Spinning Space
Cited by in corpus (34)
- Physical Aspects of the Space-Time Torsion
- Black holes, hidden symmetries, and complete integrability
- Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
- On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
- Generalized Killing-Yano equations in D=5 gauged supergravity
- Generalized hidden symmetries and the Kerr-Sen black hole
- Symmetries of the Dirac operator with skew-symmetric torsion
- Killing-Yano tensors and some applications
- Killing-Yano Supersymmetry in String Theory
- Anholonomic Frames, Generalized Killing Equations, and Anisotropic Taub NUT Spinning Spaces
- Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor
- Hidden symmetry in the presence of fluxes
- Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general non-extremal rotating charged black holes in minimal five-dimensional gauged supergravity
- Higher order first integrals of motion in a gauge covariant Hamiltonian framework
- Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory
- Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
- Gravitational Theory with a Dynamical Time
- Killing tensors in pp-wave spacetimes
- Principal Tensor Strikes Again: Separability of Vector Equations with Torsion
- An index theorem for non-standard Dirac operators
- Dynamical supersymmetry of spin particle-magnetic field interaction
- Dual Metrics and Non-Generic Supersymmetries for a Class of Siklos Spacetimes
- Generalized particle dynamics: modifying the motion of particles and branes
- Dual Metrics for a Class of Radiative Spacetimes
- Geometrization of the Lax Pair Tensors
- Schouten-Nijenhuis bracket of Killing-Yano tensors for Kimura IIC metric
- Killing-Yano tensors and surface terms
- Generalized particle dynamics in anti de Sitter spaces: A source for dark energy
- Entangled spinning particles in charged and rotating black holes
- Higher-dimensional lifts of Killing-Yano forms with torsion
- Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields
- Kerr-Schild transformation of the Benenti-Francaviglia metric
- f-symbols in Robertson-Walker space-times
- f-symbols, Killing tensors and conserved Bel-type currents