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.