Speaker
Description
In this talk, I will show how we used the covariant $1/c$-expansion to construct a framework for post-Newtonian gravity that is valid in any gauge with a Newtonian regime. This is not true for every gauge as Newtonian gravity itself is a gauge fixed version of Newton-Cartan gravity. Thus, we fix the leading order gauge choice but keep full gauge freedom at all subleading orders in this framework. Due to the limited region of validity of the PN expansion, we have to construct a similarly covariant (for all post-Newtonian gauges) framework for the multipolar post-Minkowskian expansion outside the compact matter source. This is then glued together with the PN expansion through matched asymptotic expansion methods. This framework stands in contrast to the standard Blanchet-Damour approach which relies entirely on the harmonic gauge. I will show how this new framework allows us to make general statements about the structure of the equations at any order and write down the full field equations to 2.5PN order, valid for any PN gauge. I will then go on to showcase the framework in what we refer to as transverse gauge and explain why this could be an interesting alternative to the standard harmonic gauge. Particularly, I will highlight how this gauge reduces the number of relativistic wave equations (exchanging them for the simpler Poisson equation) that one has to solve for in MPM expansion as well as significantly simplifying half-PN orders in the metric as compared to harmonic gauge.
