General teleparallel metrical geometries
Abstract
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.
Cite
@article{arxiv.2303.17812,
title = {General teleparallel metrical geometries},
author = {Muzaffer Adak and Tekin Dereli and Tomi S. Koivisto and Caglar Pala},
journal= {arXiv preprint arXiv:2303.17812},
year = {2023}
}
Comments
To appear in IJGMMP for special issue metric-affine gravity tartu