Symmetric teleparallel general relativity

TL;DR

This paper explores symmetric teleparallel gravity, a geometric formulation where curvature and torsion vanish but nonmetricity encodes gravity, providing a covariant and tensorial energy-momentum description of general relativity.

Contribution

It introduces and analyzes the symmetric teleparallel formulation of general relativity, emphasizing its covariant nature and tensorial energy-momentum representation.

Findings

Nonmetricity encodes gravitational force in this formulation.

Energy-momentum density becomes a true tensor.

Covariantization legitimizes coordinate calculations in gravity.

Abstract

General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its ``translational gauge theory'' nature. The standard version is metric compatible, with torsion representing the gravitational ``force''. However there are many other possibilities. Here we focus on an interesting alternate extreme: curvature and torsion vanish but the nonmetricity $\nabla g$ does not---it carries the ``gravitational force''. This {\it symmetric teleparallel} representation of general relativity covariantizes (and hence legitimizes) the usual coordinate calculations. The associated energy-momentum density is essentially the Einstein pseudotensor, but in this novel geometric representation it is a true tensor.