Abstract
A metric is given that produces a space in which the geodesic equation is identical with the Lorentz equation of motion for a charged particle. The gravitational field equations in the same space indicate a geometric origin for the electromagnetic energy-momentum tensor. A comparison is made with Kaluza-Klein theories and it is determined that the present theory is distinct from them because it corresponds to a timelike, noncompact fifth dimension. Since the metric is velocity-dependent, it is actually a Finsler space rather than a Riemannian space metric. Its special form, however, allows computations to be done in terms of Riemannian geometry.
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Beil, R.G. Electrodynamics from a metric. Int J Theor Phys 26, 189–197 (1987). https://doi.org/10.1007/BF00669600
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DOI: https://doi.org/10.1007/BF00669600