EFT approach to general relativity: correction to EIH Lagrangian due to electromagnetic charge

TL;DR

This paper extends the NRGR framework to include electromagnetic charges, deriving corrections to the EIH Lagrangian by incorporating photon interactions with charged binary constituents.

Contribution

The paper introduces a method to incorporate electromagnetic charge effects into the NRGR formalism, deriving corrected EIH Lagrangian terms.

Findings

Derived Feynman rules for photon-graviton interactions with point particles.

Calculated electromagnetic charge corrections to the EIH Lagrangian.

Extended NRGR to charged binary systems.

Abstract

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.