Non-Relativistic Gravitation: From Newton to Einstein and Back

TL;DR

This paper advances the classical effective theory approach to non-relativistic gravity by decomposing the metric into NRG-fields, simplifying derivations, and providing clear physical interpretations of spin interactions and post-Newtonian corrections.

Contribution

It introduces a decomposition of the potential metric into NRG-fields, simplifying the derivation of the Einstein-Infeld-Hoffmann Lagrangian and clarifying physical interpretations.

Findings

Simplified derivation of the Einstein-Infeld-Hoffmann Lagrangian.

Clear physical interpretation of spin interactions via gravito-magnetic field.

Presentation of leading correction diagrams for 3PN and 2.5PN interactions.

Abstract

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.