Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
Classical potential for general spinning bodies
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In the root-Kerr probe model, integrability holds to all spin orders at leading probe charge under Newman-Janis vertices but fails at spin-cubic order at second charge order and cannot be restored by further action deformation.
The work establishes conservation of several quantities in Kerr black hole scattering and presents evidence that a spinning probe satisfies asymptotic integrability to quartic spin order at all post-Minkowskian orders.
NLO angular impulse for Kerr black holes computed to all orders in spin via KMOC formalism and leading singularities, with consistency checks and potential extraction.
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