Non-Relativistic Gravitation: From Newton to Einstein and Back
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.
Keywords
Cite
@article{arxiv.0712.4116,
title = {Non-Relativistic Gravitation: From Newton to Einstein and Back},
author = {Barak Kol and Michael Smolkin},
journal= {arXiv preprint arXiv:0712.4116},
year = {2008}
}
Comments
10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introduction