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