Abstract
A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the electromagnetic field. The Einstein-Maxwell equations will also be simplified. New group isomorphisms are proved. The local group of electromagnetic gauge transformations is isomorphic to the new group LB1. LB1 is the group of local tetrad transformations comprised by SO(1,1) plus two different kinds of discrete transformations. The local group of electromagnetic gauge transformations is also isomorphic to the local group of tetrad transformations LB2, which is SO(2), as well. Therefore, we proved that LB1 is isomorphic to LB2. These group results amount to proving that the no-go theorems of the sixties like the S. Coleman- J. Mandula, the S. Weinberg or L. ORaifeartagh versions are incorrect. Not because of their internal logic, but because of the assumptions made at the outset of all these versions. These new tetrads are useful in astrophysics spacetime evolution algorithms since they introduce maximum simplification in all relevant objects, specially in stress-energy tensors.
Highlights
There is an isomorphism between kinematic states and gauge states of the gravitational fields, locally
We have proven that the local group of electromagnetic gauge transformations is isomorphic to the new group LB1
The local group of electromagnetic gauge transformations is isomorphic to the local group of tetrad transformations LB2 as well
Summary
The only difference in notation with Ref.[1] will be that we will call our geometrized electromagnetic potential Aμ, where fμν = Aν;μ − Aμ;ν. This is an Open Access article published by World Scientific Publishing Company. The local duality rotation given by Eq (59) in paper[1] fμν = ξμν cos α + ∗ξμν sin α , allows us to express the stress-energy tensor in terms of the extremal field. The explicit expression for the complexion, which is a local electromagnetic gauge invariant, can be given when imposing condition (3), by tan(2α) = −fμν ∗ f μν /fλρ f λρ
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