2022/10/08 by Paul Ramond, Soichiro Isoyama, Ramond, Paul +1 · 2 citations
Engineering · #Geophysics and Sensor Technology #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2210.03866
openalex publication_date 2022/10/08 · openalex created_date 2022/10/12 · openalex updated_date 2026/07/28
We study the Hamiltonian dynamics of a neutral, massive spinning test body at linear order in spin, as governed by the Mathisson--Papapetrou--Tulczyjew--Dixon equations in a 4-dimensional spacetime admitting a non-degenerate Killing--Yano tensor. The Tulczyjew--Dixon spin supplementary condition is imposed as a set of algebraic constraints, and the resulting constraint surface is equipped with a Poisson--Dirac bracket, yielding a non-degenerate, 10-dimensional physical phase space. On this reduced space we identify five functionally independent first integrals in involution: the autonomous Hamiltonian, two constants of motion associated with two commuting Killing vectors, a generalised Carter constant, and the Rüdiger constant; all four descending from the Killing--Yano tensor. All calculations are covariant, and the result is a purely geometric statement: it requires no background field equations and holds for any metric admitting a non-degenerate Killing--Yano tensor, beyond Kerr, beyond vacuum and beyond general relativity. Our results identify Killing--Yano symmetry as the sole geometric source of linear-in-spin integrability. Extensions to quadratic-in-spin dynamics, including the spin-induced quadrupole, and to tidally-induced quadrupolar effects for non-spinning bodies, are treated in companion papers.