Effective field theory calculation of second post-Newtonian binary dynamics

TL;DR

This paper applies effective field theory to compute the second Post-Newtonian binary dynamics, demonstrating a streamlined approach that reproduces known results and tests a specific metric parametrization for computational efficiency.

Contribution

It introduces an efficient effective field theory method for second Post-Newtonian calculations and validates a particular metric parametrization for simplifying the process.

Findings

Reproduces known second Post-Newtonian equations of motion

Demonstrates advantages of temporal Kaluza-Klein metric parametrization

Provides a streamlined calculation approach

Abstract

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second Post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second Post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.