Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
arXiv:1406.3069 · doi:10.1103/PhysRevD.91.024013
Abstract
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p-1). Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.
20 pages. Some references and a conclusion section have been added in order to match the published version
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- On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
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- Uses of Killing and Killing-Yano Tensors
- Geometry, conformal Killing-Yano tensors and conserved "currents"
- On Conserved Quantities for the Free Motion of Particles with Spin
- Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
- Conserved quantities and integrability for massless spinning particles in general relativity