Non-Relativistic Gravity and its Coupling to Matter

Understand

We study the non-relativistic expansion of general relativity coupled to matter.

• This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light.
• In order to perform this expansion it is shown to be very convenient to rewrite general relativity in terms of a timelike vielbein and a spatial metric.
• This expansion can be performed covariantly and off shell.