Description
In this talk I present the covariant 1/c-expansion of general relativity and how it relates to the well-known post-Newtonian expansion. The 1/c-expansion is an expansion of general relativity around the limit in which the tangent space lightcone flattens. This differentiates the 1/c-expansion from the post-Newtonian expansion, as it does not assume the gravitational field strength to be weak a priori. Thus, the 1/c-expansion is able to capture strong gravitational effects, such as gravitational time dilation, giving rise to a new approximation of general relativity. However, the main part of this talk is going to be focused on how to filter out the strong field effects and make contact with the post-Newtonian approximation. This is an important step in understanding the 1/c-expansion and its capabilities as we, among other things, are forced to confront its limited region of validity and incorporate it into a broader approximation scheme by way of matched asymptotic expansions. Additionally, this gives us a new framework for post-Newtonian gravity based on Newton-Carton geometry, the novel feature of which is covariance. This will allow us to deviate from the standard harmonic gauge that much of modern post-Newtonian theory relies on. Finally, I will give an outlook on other potential uses of this new framework and summarise what we have learned about the covariant 1/c-expansion as a whole.
