In fact, we need the 2.5 PN field and a part of the 3 PN field (
) to evaluate the 3 PN mass-energy relation. This
does not mean that the Hadamard partie finie regularization is sufficient to derive the 3 PN equations of motion. Indeed, when
a Dirac delta distribution is adopted to achieve the point particle limit instead of the strong field point particle limit, one
needs another regularization scheme such as the dimensional regularization to derive the 3 PN equations of motion in an
unambiguous form [22
].