The equivalence between local inertial frames and electromagnetic gauge in Einstein-Maxwell theories
Alcides Garat
TL;DR
The paper establishes a piecewise isomorphism between local inertial frames and electromagnetic gauge in Einstein–Maxwell theory by constructing a tetrad that diagonalizes the stress-energy tensor using the extremal field $\xi_{\mu\nu}$ and its dual, revealing an isomorphism between the local $U(1)$ gauge group and the tetrad transformation groups LB1 and LB2 on two independent blades. It shows that boosting an object to velocity $\beta$ corresponds to a local gauge transformation with $\partial_\mu\Lambda$, and this correspondence persists under generic local Lorentz transformations through a structure-covariant reformulation of the tetrads. The results generalize to non-Abelian Yang–Mills groups via tensor products of LB1/LB2, and hold under perturbations in a local, instantaneous sense; the framework provides a unified view where inertia and gauge transformations are locally interchangeable. The work challenges traditional no-go theorems by demonstrating a robust internal–spacetime symmetry that ties local inertial structure to gauge degrees of freedom, with potential implications for covariantized descriptions of gravity plus gauge fields and for YM theories.
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.