General Relativistic Theory of Electromagnetism
In the general theory of relativity the event world is represented by the Minkowskian manifold C whose structure is determined by the distribution of the stress-energy-momentum tensors on C in accord with Einstein’s field equations. This distribution is dominated by its intrinsic part, which is due to the presence of proper mass in a material medium. The electromagnetic field, like the stress tensor field in a material medium, gives rise to only a small contribution in the stress-energy-momentum distribution. Hence we may regard the Minkowskian metric and the electromagnetic field as independent fields on C. In this sense the metrical structure and the orientation on C are determined to within an arbitrary change of gauge by the Maxwell-Lorentz ether relation. A rigorous theory of electromagnetism in the context of general relativity, however, must allow the electromagnetic field and the gravitational field to affect each other. One exact solution of the coupled system of electromagnetic field equations and gravitational field equations is summarized in the last section of this chapter.
KeywordsField Equation Uniqueness Theorem Ether Relation Duality Operator Covariant Vector
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