The effective field theory approach to gravitation

Abstract

In the light of the recent gravitational wave detections made by the LIGO and Virgo collaboration, we study the Non-Relativistic formulation of General Relativity (NRGR) with its extension to spinning compact objects. Then we extend the NRGR formalism to incorporate the effects of electromagnetic charge on 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 due to the presence of the photon field and electromagnetic charge on the constituents of the binary.