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.

arXiv commentTo appear in IJGMMP for special issue metric-affine gravity tartu

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Cited by in corpus (8)

• Study of Viable Compact Stellar Structures in Non-Riemannian Geometry
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• The non-minimally coupled symmetric teleparallel gravity with electromagnetic field
• Einstein gravity from the Einstein action: Counterterms and covariance
• Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra
• Hamiltonian surface charges in General Parallel Relativity