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Complete set of quasi-conserved quantities for spinning particles around Kerr

by Geoffrey Compère, Adrien Druart

This Submission thread is now published as SciPost Phys. 12, 012 (2022)

Submission summary

As Contributors: Geoffrey Compère · Adrien Druart
Arxiv Link: (pdf)
Date accepted: 2021-11-08
Date submitted: 2021-10-19 15:17
Submitted by: Druart, Adrien
Submitted to: SciPost Physics
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • Mathematical Physics
Approach: Theoretical


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.

Published as SciPost Phys. 12, 012 (2022)

Author comments upon resubmission

We took into account the comments of both referees. The manuscript was improved with the minor changes listed below.

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.

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