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Complete set of quasi-conserved quantities for spinning particles around Kerr
by Geoffrey Compère, Adrien Druart
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Geoffrey Compère · Adrien Druart |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2105.12454v2 (pdf) |
| Date submitted: | July 5, 2021, 3:19 p.m. |
| Submitted by: | Adrien Druart |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-9-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2105.12454v2, delivered 2021-09-01, doi: 10.21468/SciPost.Report.3476
Report
Requested changes
- Author's explanation for their notion of quasi-conserved quantity on page 1 is rather confusing: "They are quasi-conserved in the sense that they are no longer conserved at quadratic order in the spin without further corrections". I encourage authors to give the exact and clear definition of what they mean by "quasi-conserved" quantity.
Report #1 by Anonymous (Referee 1) on 2021-8-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2105.12454v2, delivered 2021-08-15, doi: 10.21468/SciPost.Report.3392
Strengths
- The article addresses a very important question.
- The article performs a strong technical analysis.
- The article is very well written.
Weaknesses
Report
I would recommend one addition that would be beneficial to the readers. The article reduces the criterion for integrability to existence of "mixed-symmetry Killing tensors", and they demonstrate that such objects don't exist for the Kerr geometry. It would be interesting to add a small section before VII with some examples of spaces with mixed-symmetry tensors and the resulting integrability. The examples can be as simple as flat space, but I think that they would provide an excellent illustration of the formalism. I leave this addition to the authors' discretion, and I recommend this paper for publication.
Requested changes
The proposed optional change is mentioned in the report.
We thank the referee for his/her comments and suggestion. We plan to improve the manuscript with the proof that all mixed-symmetry Killing tensors of Minkowski spacetime are trivial. We will 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.
Author: Adrien Druart on 2021-09-06 [id 1738]
(in reply to Report 2 on 2021-09-01)We thank the referee for his/her comment. We plan to improve the manuscript with a rephrased the definition of quasi-conservation.