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A note on post-Riemannian structures of spacetime

Friedrich W. Hehl·Uwe Muench
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Abstract

A four-dimensional differentiable manifold is given with an arbitrary linear connection $Γ_α^β=Γ_{iα}^βdx^i$. Megged has claimed that he can define a metric $G_{αβ}$ by means of a certain integral equation such that the connection is compatible with the metric. We point out that Megged's implicite definition of his metric $G_{αβ}$ is equivalent to the assumption of a vanishing nonmetricity. Thus his result turns out to be trivial.

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Friedrich W. Hehl, Uwe Muench. 1997-08-05. A note on post-Riemannian structures of spacetime. https://arxiv.org/abs/gr-qc/9708007

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