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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Authors define Kerr generating functions for all-loop scattering on Kerr black holes and apply them to compute leading non-linear tidal effects of neutron stars up to four loops in gravity.
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.
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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.