New Tetrads in Riemannian Geometry and New Ensuing Results in Group Theory, Gauge Theory and Fundamental Physics in Particle Physics, General Relativity and Astrophysics

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.