Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit

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We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.