Weyl geometry and gauge-invariant gravitation

TL;DR

This paper develops a gauge-invariant gravitational theory within Weyl Integrable Space-Times, demonstrating its consistency with General Relativity and exploring its physical implications through exact solutions and thermodynamical analysis.

Contribution

It introduces a gauge-invariant formulation of gravitation in Weyl geometry, clarifies the role of proper-time, and provides new solutions illustrating the theory's physical significance.

Findings

All predictions of General Relativity are recovered.

A new exact cosmological solution is presented.

The physical significance of geometric fields is demonstrated.

Abstract

We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with space-time description. As a consequence of this relation and the theory's gauge symmetry we recover all predictions of General Relativity. This feature is made even clearer by a new exact solution we provide which reveals the importance of a well defined proper-time. The thermodynamical description of the source fields is given and we observe that each of the geometric fields have a certain physical significance, despite the gauge-invariance. This is shown by two examples, where one of them consists of a new cosmological constant solution. Our conclusions highlight the intimate relation among test particles trajectories, proper-time and space-time description which can also be applied in any other situation, whether or not it recovers General Relativity results and also in the absence of a gauge symmetry.