Dynamical symmetry breaking in geometrodynamics

Abstract: We are going to analyze through a first order perturbative formulation the local loss of symmetry when a source of electromagnetic and gravitational field interacts with an agent that perturbes the original geometry associated to the source. As the symmetry in Abelian or even non-Abelian field structures in four dimensional Lorentzian spacetimes is displayed through the existence of local planes of symmetry that we previously called blades one and two, the loss of symmetry will be manifested by the tilting of these planes under the influence of the external agent. In this strict sense the original local symmetry will be lost. But we will prove that the new blades at the same point will correspond after the tilting generated by perturbation to a new symmetry. The point of this note is to prove that the geometrical manifestation of local gauge symmetries is dynamic. The local original symmetries will be lost, nonetheless new symmetries will arise. There is a dynamic evolution of local symmetries.