Torsion formulation of gravity

TL;DR

This paper presents a torsion-based formulation of gravity that extends the standard theory, enabling new topologies and coupling torsion to gauge fields without losing gauge invariance.

Contribution

It introduces a precise formulation of gravity with torsion as solutions to Einstein equations, allowing for topological diversity and gauge-invariant torsion coupling.

Findings

Enables topologies excluded in standard gravity

Allows coupling of arbitrary torsion to gauge fields

Maintains gauge invariance in torsion formulations

Abstract

We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.