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Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, “Scattering Amplitudes and Conservative Binary Dynamics at 𝒪 ⁡ ( G 4 ) {\cal O}(G^{4}) ,” Phys. Rev. Lett
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2023

Kerr binary dynamics from minimal coupling and double copy

Alessio, Francesco

Understand

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects.

The construction relies on the introduction of a new covariant derivative, which we name "classical spin covariant derivative", that is compatible with the three-point interaction of the $\sqrt{\mathrm{Kerr}}$ solution with the gauge field.
The resulting Lagrangian, beside the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles.
Using double-copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin.