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.
N3LO spin-orbit interaction via the EFT of spinning gravitat- ing objects
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The NLO gravitational spin-orbit Hamiltonian for N spinning bodies is computed via PN-EFT, with only three-body diagrams new beyond the binary case, and the result matches the known ADM Hamiltonian up to canonical transformation.
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
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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.