On the triviality of certain non-Riemannian models of gravitation

TL;DR

This paper demonstrates that in a specific approach to non-Riemannian gravity, certain homogeneous Lagrangians do not influence the Einstein equations, simplifying the understanding of such models.

Contribution

It proves that homogeneous Lagrangians of order two or higher in the Tucker-Wang approach do not affect the Einstein equations, clarifying the role of these Lagrangians in non-Riemannian gravity.

Findings

Homogeneous Lagrangians of order ≥2 contribute nothing to Einstein equations.

The result applies broadly within the Tucker-Wang framework.

Other important cases are also analyzed using this result.

Abstract

We prove in the Tucker-Wang approach to non-Riemannian Gravity that a general homogeneous Lagrangian density in the general connection with order of homogeneity of at least two, gives no contribution to the generalised Einstein equations. Using this result other important cases are also considered.