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We use effective field theory techniques to compute the potentials due to spin-spin and spin-orbit effects, from which the spin(1)spin(2) contribution to the motion of spinning compact binaries to third Post-Newtonian (PN) order follow.
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R. A. Porto, “New results at 3PN via an effective field theory of gravity”. Proceedings of the 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, arXiv:gr-qc/0701106
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