Newton—Cartan gravity is a differential-geometric reformulation of Newtonian gravity, bringing the latter closer to general relativity (GR): as in GR, gravitational effects are encoded into spacetime geometry, which however is of non-Lorentzian nature. Newton—Cartan gravity can be shown to be the Newtonian limit of GR in a rigorous sense, hence providing a coordinate-free geometric formulation of this limiting process.
In this talk, after giving a brief introduction to standard Newton—Cartan gravity, we are going to discuss a `teleparallelised' version of Newton—Cartan gravity. We show how this theory arises as a formal large-speed-of-light limit of the so-called teleparallel equivalent of general relativity (TEGR). Thus, it provides a geometric formulation of the Newtonian limit of TEGR, analogous to the GR case. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered.
