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Conserved quantities and integrability for massless spinning particles in general relativity

Lars Andersson1,*, Finnian Gray2,†, and Marius A. Oancea2,‡

  • *Contact author: lars.andersson@uni-potsdam.de
  • †Contact author: finnian.gray@univie.ac.at
  • ‡Contact author: marius.oancea@univie.ac.at
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Phys. Rev. D 113, 064061 – Published 31 March, 2026

DOI: https://doi.org/10.1103/85dv-n8tr

Abstract

In general relativity, the dynamics of spinning particles is governed by the Mathisson-Papapetrou-Dixon equations, which are most commonly applied to massive bodies, but the framework also works in the massless case. Such massless versions naturally arise, for example, in the description of energy centroids of high-frequency wave packets. In this work, we consider massless spinning particles in spacetimes with hidden symmetries and we derive the generalized conservation laws associated with conformal Killing-Yano tensors. We then show that the spin Hall equations, a particular case of the Mathisson-Papapetrou-Dixon equations restricted to massless particles with longitudinal angular momentum, are completely integrable in a large class of type D spacetimes. Additionally, we also show that for massive spinning particles, the generalized Carter constant associated with Killing-Yano tensors is conserved independently of the choice of spin supplementary condition.

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Phys. Rev. D 113, 064061– Published 31 March, 2026
  • Received 23 December 2025
  • Accepted 25 February 2026
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