We study the equation of motion appropriate to an inspiralling 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 point-like
particle with strong internal gravity without using Dirac delta distribution.
Besides 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 Damour and 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.Comment: 48 pages, revtex, accepted for publication in Phys. Rev.
