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We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects.
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W. D. Goldberger, “Les Houches lectures on effective field theories and gravitational radiation,” arXiv:hep-ph/0701129
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R. A. Porto, “New results at 3PN via an effective field theory of gravity,” arXiv:gr-qc/0701106
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