A note on post-Riemannian structures of spacetime

TL;DR

This paper critiques Megged's claim that a metric compatible with a given linear connection can be defined via an integral equation, showing that his approach implicitly assumes zero nonmetricity, making the result trivial.

Contribution

The paper clarifies that Megged's proposed metric definition implicitly assumes vanishing nonmetricity, revealing the triviality of his claim.

Findings

Megged's integral equation implies zero nonmetricity

The supposed metric compatibility is trivial under the implicit assumption

The paper clarifies misconceptions about post-Riemannian structures

Abstract

A four-dimensional differentiable manifold is given with an arbitrary linear connection $\Gamma_\alpha^\beta=\Gamma_{i\alpha}^\beta dx^i$. Megged has claimed that he can define a metric $G_{\alpha\beta}$ 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 $G_{\alpha\beta}$ is equivalent to the assumption of a vanishing nonmetricity. Thus his result turns out to be trivial.