Can the Kerr Solution Be Found by the Einstein–Infeld–Hoffmann Method?

We present expansions of the Kerr metric in harmonic coordinates for the values of the radial coordinate $r$ at which the dimensionless parameters $m/r$ and $a/r$ ($m$ and $a$ are parameters used in the Kerr solution) are of the respective second and first orders of smallness. We show that it is impossible to obtain these expansions uniquely using the Einstein–Infeld–Hoffmann method. We conclude that we must normalize the Kerr metric expansions for the expressions obtained in deriving the equations of translational motion of particle singularities and the evolution equations of their spins in the post-Newtonian and higher-order approximations.