Conserved quantities and integrability for massless spinning particles in general relativity
arXiv:2512.07677 · doi: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.
References in corpus (58)
- Spin-orbit interactions of light
- Transverse and longitudinal angular momenta of light
- Geometrodynamics of Spinning Light
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- A new look at the Plebanski-Demianski family of solutions
- Black holes, hidden symmetries, and complete integrability
- Spin Hall effect of Photons in a Static Gravitational Field
- Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime
- Fermat Principle for spinning light
- Gravitational spin Hall effect of light
- Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
- Mechanics of extended masses in general relativity
- On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
- Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
- Mathisson's helical motions for a spinning particle --- are they unphysical?
- Center of mass, spin supplementary conditions, and the momentum of spinning particles
- Self-Force Calculations with a Spinning Secondary
- Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes
- Hamilton-Jacobi equation for spinning particles near black holes
- Propagation of polarized gravitational waves
- Motion in classical field theories and the foundations of the self-force problem
- Waveform Modelling for the Laser Interferometer Space Antenna
- Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
- An intrinsic characterization of the Kerr metric
- Approximate spacetime symmetries and conservation laws
- Spin Hall effect of gravitational waves
- Maxwell equations in a curved spacetime: Spin optics approximation
- Second order symmetry operators
- Semiclassical analysis of Dirac fields on curved spacetime
- Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
- Complete set of quasi-conserved quantities for spinning particles around Kerr
- Kerr black hole in a uniform Bertotti-Robinson magnetic field: An exact solution
- Gravitational birefringence of light in Robertson-Walker cosmologies
- Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
- Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
- Frequency- and polarization-dependent lensing of gravitational waves in strong gravitational fields
- Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
- Probing general relativistic spin-orbit coupling with gravitational waves from hierarchical triple systems
- New class of rotating charged black holes with nonaligned electromagnetic field
- A simple test for spacetime symmetry
- Spin Hall effects in the sky
- Massless spinning test particles in vacuum algebraically special spacetimes
- Symmetry operators and decoupled equations for linear fields on black hole spacetimes
- Spin geometry and conservation laws in the Kerr spacetime
- Spin wave optics for gravitational waves lensed by a Kerr black hole
- Revisiting black holes of algebraic type D with a cosmological constant
- Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
- Weyl geometric effects on the propagation of light in gravitational fields
- On integrability of the Killing equation
- Conformal invariance, complex structures, and the Teukolsky connection
- Black holes of type D revisited: relating their various metric forms
- On the integrability of extended test body dynamics around black holes
- Gravitational wave memory and its effects on particles and fields
- Spinning particles in vacuum spacetimes of different curvature types: Natural reference tetrads, and massless particles
- Gravity-induced birefringence in spherically symmetric spacetimes
- On the geometry of Petrov type II spacetimes
- Spinoptics in the Kerr Spacetime: Polarized Wave Scattering
- Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes