Teleparallel Newton-Cartan gravity

We discuss a teleparallel version of Newton-Cartan gravity. This theory arises as a formal large-speed-of-light limit of the teleparallel equivalent of general relativity (TEGR). Thus, it provides a geometric formulation of the Newtonian limit of TEGR, similar to standard Newton-Cartan gravity being the Newtonian limit of general relativity. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered.

Automated summary

We discuss a teleparallel version of Newton-Cartan gravity, which arises as a large-speed-of-light limit of the teleparallel equivalent of general relativity (TEGR). It provides a geometric formulation of the Newtonian limit of TEGR, similar to how standard Newton-Cartan gravity is the Newtonian limit of general relativity. By a specific gauge-fixing, we show how the standard formulation of Newtonian gravity can be recovered.