  We extend the Non-Relativistic formulation of General Relativity (NRGR) given
in Goldberger et al. (Phys Rev D 73:104029, 2006) to incorporate the effects of
electromagnetic charge of the constituents of the binary. We incorporate the
photon field in NRGR by giving the field decomposition and power counting
rules. Using these, we develop the Feynman rules to describe photon and
graviton interactions with point particle worldline. We then find the
corrections to the Einstein-Infeld-Hoffmann Lagrangian (Einstein et al. in Ann
Math 39:65-100, 1938) due to the presence of the photon field and
electromagnetic charge of the constituents of the binary.
