General teleparallel metrical geometries

In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity. These so called general teleparallel geometries may also have applications in material physics, such as the study of crystal defects. In this work, we explore the general teleparallel geometry in the language of differential forms. We discuss the special cases of metric and symmetric teleparallelisms, clarify the relations between formulations with different gauge fixings and without gauge fixing, and develop a method of recasting Riemannian into teleparallel geometries. As illustrations of the method, exact solutions are presented for the generic quadratic theory in 2, 3 and 4 dimensions.

Automated summary

In the conventional formulation of general relativity, gravity is described by metric curvature. However, there are alternative formulations in flat affine geometries using torsion and nonmetricity. These general teleparallel geometries have potential applications in material physics, such as the study of crystal defects. This work explores the general teleparallel geometry using differential forms, discusses different gauge fixings, and presents exact solutions for the quadratic theory in 2, 3, and 4 dimensions.