Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion

Abstract

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. We use a formalism which allows us to impose the spin supplementarity condition (SSC) in a canonical framework to all orders in the PN expansion. We explicitly show the equivalence with our previous results, obtained using the Newton-Wigner SSC at the level of the action for spin-spin and spin-orbit potentials reported in arXiv:gr-qc/0604099 and arXiv:0712.2032[gr-qc] respectively.

Comments: 31 pages, 3 figures. v4: All the irrelevant (spin-independent) terms in eqs (22) and (23) are now omitted, as in eqs (24) and (25), to avoid any possible confusion regarding the self-consistency of the tetrad ('ee=g'). The procedure and results in the paper are unaltered