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Abstract

We discuss the Hamiltonian for the conservative dynamics of generic-orbit arbitrary-mass-ratio spinning binary black holes, at the leading post-Newtonian orders at each order in an expansion in spins, to all orders in the spins. The leading-order couplings can all be obtained from a map to the motion of a test black hole (a test body with the spin-induced multipoles of a Kerr black hole) in the Kerr spacetime, as is confirmed with direct post-Newtonian calculations for arbitrary mass ratios. Furthermore, all of the couplings can be "deduced" from those of a pole-dipole test body in Kerr.