UCLA

This dissertation investigates the dynamics of a charged, spinning probe governed by the Mathisson-Papapetrou-Dixon equations in the Root Kerr background: The electromagnetic spinning-disk solution obtained from the 𝐺 → 0 limit of Kerr-Newman. Root Kerr is related by the classical double copy to the Kerr spacetime, providing an electromagnetic analogue of this gravitational solution. I find generalizations of the “hidden” Carter and Rudiger constants, showing the probe motion to be Liouville integrable through quadratic order in the probe spin. Their existence uniquely constrains the probe’s multipole moments to those of the stationary Root Kerr field and requires its leading-order dynamical moments to vanish. These results further determine the corresponding classical Compton amplitude through spin squared, exhibiting spin exponentiation and agreeing with the classical limit of a minimally coupled Compton, derived through little group scaling and amplitude factorization. The failure of integrability beyond quadratic spin order indicates that hidden symmetries cannot provide a general principle for determining higher-order dynamical multipole moments or the associated Compton amplitude.