New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity

A third post-Newtonian (3PN) equation of motion for an inspiraling binary consisting of two spherical compact stars with strong internal gravity is derived under the harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in the sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits the conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3PN equation of motion and an energy of the binary orbital motion in the case of a circular orbit (neglecting the 2.5PN radiation reaction effect) and in the center of mass frame. It is argued that the 3PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.