The equivalence between local inertial frames and electromagnetic gauge in Einstein-Maxwell theories

TL;DR

This paper proves the local equivalence of inertial frames and electromagnetic gauge states in Einstein-Maxwell theories, showing that boosting matter is akin to a gauge transformation, thus linking spacetime symmetries and gauge invariance.

Contribution

It establishes a formal isomorphism between local Lorentz transformations and electromagnetic gauge transformations in Einstein-Maxwell theories.

Findings

Local inertial frames and gauge states are equivalent in Einstein-Maxwell theories.

Boosting matter corresponds to a gauge transformation.

Theorems relate electromagnetic stress-energy tensors to tetrad transformations.

Abstract

It has been proven that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof is valid for Einstein-Maxwell theories in four-dimensional Lorentzian spacetimes. Use will be made of theorems proved in a previous manuscript. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local group of Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress-energy tensor. Two isomorphisms, one for each orthogonal plane of stress-energy eigenvectors. We will discuss the opposite problem in this paper. What happens with local electromagnetic gauge when the test object under study is boosted by any mechanical means. We will prove that boosting matter is indistinguishable from introducing an appropriate local electromagnetic gauge transformation.