Internal-structure dependent coefficients in the post-Newtonian equations of motion

Physics

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Scientific paper

The post-3-Newtonian equation of motion for "point particles" recently derived by Damour, Jaranowski and Schafer and by Blanchet and Faye contains a term whose numerical coefficient has not yet been determined by the methods used to date to derive the equations of motion. One might speculate that the coefficient depends on the internal structure of the bodies, so that, for example, it would have different values for polytropic stellar models with different polytropic indices. We show here that this is not the case -- the coefficient must take the same value for all spherically symmetric bodies -- and that such internal-structure dependent coefficients cannot arise at orders below the 5th post Newtonian order. The argument is based on an earlier, matched asymptotic expansion based analysis of the interaction of the orbital motion and internal degrees of freedom in binary stellar systems.

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