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B.3 Quadrupole-orbit coupling force

The quadrupole-orbit coupling force can be derived by evaluating the following integral
∮ Fi = − dSj 8[(− g)tij] + ..., (225 ) 1QO ∂B1 LL
with ij i j j i ij ττ,k ττ,l 8[(− g )tLL] = (δkδl + δkδl + − δ δkl)4h 8h ∕4 + .... Then we have the quadrupole-orbit coupling force in the same form as the result in [152Jump To The Next Citation Point],
3 ( ) ( ) F1iQO = ε4--4- m1I2⟨kl⟩+ m2I ⟨1kl⟩ 2δilnk12 − 5ni12nk12nl12 . (226 ) 2r12
This result agrees formally with the Newtonian quadrupole-orbit coupling force, see Equation (58View Equation).
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"The Post-Newtonian Approximation for Relativistic Compact Binaries"
Toshifumi Futamase and Yousuke Itoh
http://www.livingreviews.org/lrr-2007-2		 Creative Commons License
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