The binary black-hole dynamics at the third post-Newtonian order in the orbital motion

The orbital dynamics of the binary point-mass systems is ambiguous at the third post-Newtonian order of approximation. The static ambiguity is known to be related to the difference between the Brill-Lindquist solution and the Misner-Lindquist solution of the time-symmetric conformally flat initial value problem for binary black holes. The kinetic ambiguity is noticed to violate in general the standard relation between the center-of-mass velocity and the total linear momentum as demanded by global Lorentz invariance.