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

Abstract

The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic 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.

17 pages. v5: Added section 4 providing the harmonic gauge fixing term in NRG fields and appendix A with a derivation of the action

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