The Parametrized Post-Newtonian (PPN) formalism is used to prove that metric theories which have post-Newtonian integral conservation laws for energy, momentum, angular momentum, and center-ofmass motion must be of a particular form, i.e., their PPN parameter values must obey certain constraints. These constraints leave only two PPN parameters freely specifiable. It is also shown that the post-Newtonian metric of any theory of gravity is invariant under a postGalilean transformation if and only if its PPN parameters A1, A2, Pi, and satisfy a set of constraints. A theory which satisfied these parameter constraints would then give the same results for any computation involving gravity, no matter what asymptotically Lorentz coordinate system were used. For theories which do possess conservation laws, the transformation properties of the conserved integral quantities under post- Galilean transformations are determined.
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Clifford M. Will (1971) studied this question.