Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order

We compute the radiation-reaction force on the orbital motion of compact binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order beyond the dominant effect. The method is based on a direct PN iteration of the near-zone metric and equations of motion of an extended isolated system, using appropriate 'asymptotically matched' flat-spacetime retarded potentials. The formalism is subsequently applied to binary systems of point particles, with the help of the Hadamard self-field regularization. Our result is the 3.5PN acceleration term in a general harmonic coordinate frame. Restricting the expression to the centre-of-mass frame, we find perfect agreement with the result derived in a class of coordinate systems by Iyer and Will using the energy and angular-momentum balance equations.