  We are going to prove that locally the inertial frames and gauge states of
the electromagnetic field are equivalent. This proof will be 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 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 plane defined locally by
two separate sets of two vectors each. In particular, we are going to use the
plane defined by the timelike and one spacelike vector, plane or blade one.
These results will be extended to any tetrad that results in a local Lorentz
transformation of the special tetrad that locally and covariantly diagonalizes
the stress-energy tensor.
