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Complete set of quasi-conserved quantities for spinning particles around Kerr
by Geoffrey Compère, Adrien Druart
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Submission summary
| Authors (as registered SciPost users): | Geoffrey Compère · Adrien Druart |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2105.12454v3 (pdf) |
| Date accepted: | 2021-11-08 |
| Date submitted: | 2021-10-19 15:17 |
| Submitted by: | Druart, Adrien |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by R\"udiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.
Author comments upon resubmission
List of changes
- A rephrased the definition of quasi-conservation;
- The proof that all mixed-symmetry Killing tensors of Minkowski spacetime are trivial. We leave the investigation of mixed-symmetry Killing tensors for (anti-)de Sitter spacetimes for further work since it is not really related to the topic of this paper.
Published as SciPost Phys. 12, 012 (2022)