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.
Comment on `On the next-to-leading order gravitational spin(1)-spin(2) dynamics' by J. Steinhoff et al
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In this comment we explain the discrepancy found between the results in arXiv:0712.1716v1 for the 3PN spin-spin potential and those previously derived in gr-qc/0604099. We point out that to compare one must include sub-leading lower order spin-orbit effects which contribute to the spin-spin potential once one transforms to the PN frame. When these effects are included the results in arXiv:0712.1716v1 do indeed reproduce those found in gr-qc/0604099.
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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.