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.
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Scattering angles in Kerr metrics
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Twisted Feynman integrals are introduced with graded Symanzik polynomials, classified as exponential periods, and shown to have geometry not inferable from generalized Baikov leading singularities.
In five dimensions, minimally coupled massive vector and antisymmetric tensor fields produce only mass or stress quadrupoles respectively from scattering amplitudes, failing to match the Myers-Perry black hole and demonstrating breakdown of spin universality.
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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Generalized Carter & R\"udiger Constants of $\sqrt{\text{Kerr}}$
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.