A possible gauge formulation for gravity?

TL;DR

This paper explores a gauge-theoretic formulation of gravity inspired by Yang-Mills theories, proposing a metric as a gauge map and connecting it to Einstein's theory, with solutions consistent with Newtonian gravity.

Contribution

It introduces a novel gauge formulation for gravity based on specific assumptions, linking it to Einstein's theory and classical limits.

Findings

Stationary solutions in the abelian case for spherical symmetry

Connection to Möller's Maxwell-like gravity formulation

Consistency with Newtonian gravity in the classical limit

Abstract

A possible Yang-Mills like lagrangian formulation for gravity is explored. The starting point consists on two next assumptions. First, the metric is assumed as a real map from a given gauge group. Second, a gauge invariant lagrangian density is considered with the condition that it is related to the Einstein one up to a bound term. We study a stationary solution of the abelian case for the spherical symmetry, which is connected to the M\"oller's Maxwell like formulation for gravity. Finally, it is showed the consistence of this formulation with the Newtonian limit.