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arXiv · gr-qc/9809049

Symmetric teleparallel general relativity

J. M. Nester·H-J Yo
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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.

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J. M. Nester, H-J Yo. 1999-02-24. Symmetric teleparallel general relativity. https://arxiv.org/abs/gr-qc/9809049

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