Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order - art. no. 044006

We derive spin-orbit coupling effects on the gravitational field and equati ons of motion of compact binaries in the 2.5 post-Newtonian approximation t o general relativity, one PN order beyond when spin effects first appear. O ur method iu based on that of Blanchet, Faye, and Ponsot, who use a past-Ne wtonian metric valid for general (continuous) fluids and represent pointlik e compact objects with a delta -function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtoni an spin effects, we use a different delta -function stress-energy tensor in troduced by Bailey and Israel. In a future paper we will use the 2.5PN equa tions of motion For spinning bodies to derive the gravitational-wave lumino sity and phase evolution of binary inspirals, which will be useful in const ructing matched filters for signal analysis. The gravitational field derive d here may help in posing initial data for numerical evolutions of binary b lack hole mergers.