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We demonstrate equivalences, under simple mappings, between the dynamics ofthree distinct systems---(i) an arbitrary-mass-ratio two-spinning-black-holesystem, (ii) a spinning test black hole in a background Kerr spacetime, and(iii) geodesic motion in Kerr---when each is considered in the firstpost-Minkowskian (1PM) approximation to general relativity, i.e. to linearorder $G$ but to all orders in $1/c$, and to all orders in the black holes'spins, with all orders in the multipole expansions of their linearizedgravitational fields. This is accomplished via computations of the net resultsof weak gravitational scattering encounters between two spinning black holes,namely the net $O(G)$ changes in the holes' momenta and spins as functions ofthe incoming state. The results are given in remarkably simple closed forms,found by solving effective Mathisson-Papapetrou-Dixon-type equations of motionfor a spinning black hole in conjunction with the linearized Einstein equation,with appropriate matching to the Kerr solution. The scattering results fullyencode the gauge-invariant content of a canonical Hamiltonian governingbinary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbitsand spin orientations. We deduce one such Hamiltonian, which reproduces andresums the 1PM parts of all such previous post-Newtonian results, and whichdirectly manifests the equivalences with the test-body limits via simpleeffective-one-body mappings.

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings