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The concept of charge is developed relativistically by assuming that there is a linear relation between point charge (e) and point mass (m) of the type: [Formula: see text] where ζ is a scalar parameter which is unchanged in all reference frames. The theory shows that charge, in a relativistic development based on this hypothesis, depends in general on the velocity of the particle carrying the charge, and the latter vanishes at the speed of light. The hypothesis (1) also implies that charge depends on the scalar and vector potentials of the electromagnetic field. These conclusions are in qualitative agreement with experimental observation.

A rigorous proof is given of the Evans lemma of general relativity and differential geometry. The lemma is the subsidiary proposition leading to the Evans wave equation and proves that the eigenvalues of the d'Alembertian operator, acting on any differential form, are scalar curvatures. The Evans wave equation shows that the eigenvalues of the d'Alembertian operator, acting on any differential form, are eigenvalues of the index-contracted canonical energy momentum tensor T multiplied by the Einstein constant k. The lemma is a rigorous and general result in differential geometry, and the wave equation is a rigorous and general result for all radiated and matter fields in physics. The wave equation reduces to the main equations of physics in the appropriate limits, and unifies the four types of radiated fields thought to exist in nature: gravitational, electromagnetic, weak and strong.