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

Geoffrey Compère, Adrien Druart

SciPost Phys. 12, 012 (2022) · published 10 January 2022

- doi: 10.21468/SciPostPhys.12.1.012
- Submissions/Reports

### 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.

### Cited by 7

### Authors / Affiliation: mappings to Contributors and Organizations

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^{1}Geoffrey Compère, -
^{1}Adrien Druart

- Fonds De La Recherche Scientifique - FNRS (FNRS) (through Organization: Fonds National de la Recherche Scientifique [FNRS])