Teleparallel gravity

Abstract: In general relativity, the only dynamical field describing the gravitational interaction of matter, is the metric. It induces the causal structure of spacetime, governs the motion of physical bodies through its Levi-Civita connection, and mediates gravity via the curvature of this connection. While numerous modified theories of gravity retain these principles, it is also possible to introduce another affine connection as a fundamental field, and consider its properties - curvature, torsion, nonmetricity - as the mediators of gravity. In the most general case, this gives rise to the class of metric-affine gravity theories, while restricting to metric-compatible connections, for which nonmetricity vanishes, comprises the class of Poincar\'e gauge theories. Alternatively, one may also consider connections with vanishing curvature. This assumption yields the class of teleparallel gravity theories. This chapter gives a simplified introduction to teleparallel gravity, with a focus on performing practical calculations, as well as an overview of the most commonly studied classes of teleparallel gravity theories.