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arxiv: gr-qc/9809049 · v2 · submitted 1998-09-17 · 🌀 gr-qc

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Symmetric teleparallel general relativity

J.M. Nester , H-J Yo (National Central U.)
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classification 🌀 gr-qc
keywords generalrelativityteleparallelcurvatureenergy-momentumforcegravitationalother
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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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