Equation of motion for relativistic compact binaries with the strong field point particle limit: The second and half post-Newtonian order

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Abstract
We study the equation of motion appropriate to an inspiraling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can introduce into general relativity a notion of a pointlike particle with strong internal gravity without using the Dirac delta distribution. In addition to this limit, to deal with strong internal gravity we express the equation of motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the equation of motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This equation is derived in the harmonic coordinate. Our resulting equation perfectly agrees with the Damour-Deruelle 2.5 PN equation of motion. Hence it is found that the 2.5 PN equation of motion is applicable to a relativistic compact binary.