Singular gauge transformations in geometrodynamics

TL;DR

This paper explores the relationship between electromagnetic gauge transformations and tetrad transformations in Einstein-Maxwell spacetimes, focusing on singular gauge transformations and their geometric implications.

Contribution

It introduces a framework linking electromagnetic gauge groups to tetrad transformations on eigenvector planes, highlighting the existence and properties of singular gauge transformations.

Findings

Established connection between gauge transformations and tetrad vectors.

Identified the potential for singular gauge transformations to map vectors within light cone intersections.

Explored the mathematical and geometric structure of these transformations.

Abstract

The new tetrads introduced previously for non-null electromagnetic fields in Einstein- Maxwell spacetimes enable a direct link to the local electromagnetic gauge group of transformations. Due to the peculiar elements in the construction of these new tetrads a direct connection can be established between the local group of electromagnetic gauge transformations and local groups of tetrad transformations on two different local and orthogonal planes of eigenvectors of the Einstein-Maxwell stress-energy tensor. These tetrad vectors are gauge dependent. It is an interesting and relevant problem to study if there are local gauge transformations that can map on the timelike-spacelike plane, the timelike and the spacelike vectors into the intersection of the local light cone and the plane itself. How many of these local gauge transformations exist and how the mathematics and the geometry of these particular transformations play out. These local gauge transformations would be singular and it is important to identify them.