The 1/c expansion of general relativity in a 3+1 formulation, revisited

We study the 1/c expansion of general relativity within a formulation that is compatible with both the Arnowitt-Deser-Misner and the Kol-Smolkin decompositions. The Einstein-Hilbert action takes a common form for those decompositions as they are dual to each other. We first develop a method to expand this generic form and then push the expansion up to c−3 order within this novel approach. Next, we apply our technique to the Arnowitt-Deser-Misner decomposition and expand it up to c−3 order explicitly. In order to demonstrate the applicability of our method and to highlight the duality at the level of expansion, we also perform the expansion in the Kol-Smolkin decomposition up to c−1 order. Lastly, we make some all-order observations.