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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 g does not---it carries the ``gravitational force''. This 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.
Nester et al. (Thu,) studied this question.
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