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We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $\mathcal{O}(G^2)$ and to all orders in velocity.
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V. Vaidya, “Gravitational spin Hamiltonians from the S matrix,” Phys. Rev. D
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R. A. Porto, “The effective field theorist’s approach to gravitational dynamics,” Phys. Rept
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S. Caron-Huot and Z. Zahraee, “Integrability of Black Hole Orbits in Maximal Supergravity,” JHEP
2019
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F. Cachazo and A. Guevara, “Leading Singularities and Classical Gravitational Scattering,” JHEP
2020
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