Conserved quantities for the free motion of particles with spin

Santos, André C.; Batista, Carlos

doi:10.1103/physrevd.101.104049

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…( 9) in order to express the 4-velocity as a function of the linear momentum. It can be shown [24,32,33] that…”

Section: The Spin Supplementary Conditionmentioning

confidence: 99%

“…2 Our definition of D µ α differs by a global '−' sign from the one provided in [24] due to the convention chosen for the signature. 3 For a proposal of a completion of the MPT equations with improved ultra-relativistic behavior, see [34,35].…”

Section: The Spin Vectormentioning

confidence: 99%

“…3 For a proposal of a completion of the MPT equations with improved ultra-relativistic behavior, see [34,35]. 4 The convention chosen here differs from the one of [22,24] by a global '−' sign.…”

Section: The Spin Vectormentioning

confidence: 99%

“…It would be an invariant of the motion at all orders in the spin provided that Y satisfy a set of additional conditions [22] which have been shown by Santos and Batista [24] to be equivalent to requiring that Y is a covariantly constant Killing-Yano tensor on the background spacetime, which rules out the Kerr background. However, no systematic analysis has been performed yet on deforming the invariant Q Y with quadratic corrections in order to attempt to construct quasi-invariants at quadratic or higher order while not further restricting the background.…”

Section: State-of-the-artmentioning

confidence: 99%

“…They are quasi-conserved, i.e., conserved at linear order in the spin or, equivalently, admitting an evolution along the orbit (at least) quadratic in the spin. In fact, without further quadratic corrections, Rüdiger's quasi-constants of motion are not conserved at quadratic order in the spin [24].…”

Section: Introductionmentioning

confidence: 99%

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

Compère

Druart

2022

SciPost Phys.

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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 Rüdiger, 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.

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“…( 9) in order to express the 4-velocity as a function of the linear momentum. It can be shown [24,32,33] that…”

Section: The Spin Supplementary Conditionmentioning

confidence: 99%