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Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third Post-Newtonian order, including sub-leading self-induced finite size effects.
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For a review see W. Goldberger “Les Houches lectures on effective field theories and gravitational radiation.” Proceedings of Les Houches summer school - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, arXiv: hep-ph/0701129. Also, R. A. Porto and R. Sturani, “Scalar gravity: Post-Newtonian corrections via an effective field theory approach” Ibidem, arXiv: gr-qc/0701105
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