Einstein’s action and the harmonic gauge in terms of Newtonian fields

The Newtonian or nonrelativistic decomposition of Einstein’s gravitational field is useful in the post-Newtonian approximation. We obtain the full nonquadratic Einstein-Hilbert action in terms of these fields as well as the harmonic gauge fixing term and find fairly simple expressions. We discuss alternatives to the harmonic gauge.

Figure 1

Diagrammatic representation of the new static interaction obtained after gauging away $A^i{\nabla }_i\varphi \dot{\varphi }$ from the Einstein-Hilbert action.

Figure 2

New static Feynman diagrams obtained after gauging away $A^i{\nabla }_i\varphi \dot{\varphi }$ from the Einstein-Hilbert action. (a) and (b) replace figures 5(l) and 5(k) of Gilmore-Ross, respectively.