{
  "annotation_id": "a11ea2a4-c0f9-49a5-9d20-73e7872116f0",
  "date_created": "2026-02-17T05:53:08.716000Z",
  "date_modified": "2026-02-17T05:53:08.716000Z",
  "file_hash": "8fec5ab2c33a557412b0eb680b456eb5055199e3e0aabacc0ba44e9f803329d3",
  "private": false,
  "record": {
    "abstract": "We develop a covariant Hamiltonian formulation of the Mathisson-Papapetrou-Tulczyjew-Dixon dynamics at quadratic order in spin under the Tulczyjew-Dixon spin supplementary condition (TD SSC). In four-dimensional, type-D Einstein (vacuum/$\\Lambda$-vacuum) spacetimes admitting a non-degenerate Killing-Yano (KY) tensor, we reduce via a Dirac bracket to the 10-dimensional physical phase space and model the quadratic sector with a spin-induced quadrupole characterized by a deformability $\\kappa$ ($\\kappa=1$ for black-hole--like; $\\kappa\\neq 1$ for material or exotic compact objects). For $\\kappa=1$, we construct five independent first integrals -- an autonomous Hamiltonian, two KY-generated Killing invariants, a linear R\\\"udiger constant, and a quadratic Carter-R\\\"udiger constant -- establishing Liouville-Arnold integrability at quadratic order in spin. For $\\kappa\\neq 1$, the symmetry-generated invariants are not conserved in general and integrability does not persist at this order. The proof proceeds via covariant Poisson-bracket computations using a null bivector decomposition; Kerr is recovered as a special case. These results show that integrability can persist beyond Kerr and beyond the linear-in-spin regime, laying groundwork for symmetry-based, beyond-Kerr modelling of asymmetric-mass, spinning compact binaries.",
    "arxiv_id": "2601.06416",
    "authors": [
      "Paul Ramond",
      "Soichiro Isoyama",
      "Adrien Druart"
    ],
    "categories": [
      "gr-qc",
      "nlin.SI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown",
    "url": "https://arxiv.org/abs/2601.06416",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41938971-7e5c-4ace-8454-66621cac7fb7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}