  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.
