  The relationship between the Arnowitt-Deser-Misner (ADM) field decomposition
and the non-relativistic gravitational (NRG) fields attracted considerable
interest recently. This paper compares the two, especially with respect to
computing the two-body post-Newtonian (PN) effective action within the
effective field theory (EFT) approach. Both are space+time decompositions and
hence do better than using the standard metric. However, ADM is essentially a
reduction over space whereas NRG is essentially a reduction over time. We use a
variant of ADM which is linearly equivalent to NRG and the two are identical at
order 1PN. We compare the two at order 2PN and find that ADM requires the
computation of an additional Feynman diagram. We argue that the computational
excess will further increase at higher orders.
