Gauge Approach to The Symmetric Teleparallel Gravity

TL;DR

This paper explores a gauge-invariant gravity model based on non-Riemannian geometry with nonzero nonmetricity, providing explicit solutions and emphasizing the sufficiency of a metric ansatz for solving the field equations.

Contribution

It introduces a gauge approach to symmetric teleparallel gravity with explicit solutions, highlighting the role of nonmetricity in a non-Riemannian framework.

Findings

Derived a conformally flat solution in the model

Showed nonmetricity is key in the geometry

Demonstrated metric ansatz sufficiency for solutions

Abstract

We discuss a gauge invariant gravity model in a non-Riemannian geometry in which the curvature and the torsion both are zero, the nonmetricity is nonzero. We also argue that only a metric ansatz is enough to start finding solutions to the field equations. As an application we obtain explicitly a conformally flat solution.