A new approach to post-Newtonian gravity

Abstract

In the thesis we consider the classic problem of a compact matter source (a perfect fluid) that evolves under the assumption of slow motion and weak gravitational field. The non-relativistic evolution of the system leads to a separation of scales. This allows us to solve for the metric near the source (the near zone) using a post-Newtonian expansion while outside (the exterior zone) the source we apply a multipolar post-Minkowskian expansion. Due to the separation of scales the exterior zone and the near zone will overlap which allows us to glue the two expansions together using matched asymptotic expansion methods. Standard approaches like that of Blanchet-Damour or the DIRE approach rely entirely on harmonic gauge. In this thesis we set up the framework to allow for any gauge with a Newtonian regime which we will refer to as post-Newtonian gauges. With this we are able to make broad statements about the structure of the expansion and the equations of motion in any post-Newtonian gauge and to arbitrary orders in both the near zone and the exterior zone expansions. We check that our framework correctly reproduces the near zone metric in harmonic gauge to 2.5 post-Newtonian order. Finally, we apply our framework to the transverse gauge which can be thought of as the general relativity equivalent of the Coulomb gauge in electromagnetism. We explicitly compute the near zone metric in transverse gauge to 2.5 post-Newtonian order as well as the far zone metric up to 1 post-Newtonian order beyond the quadrupole formula