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- W2029209314 abstract "Any skew-symmetric tensor field on a four-dimensional pseudo-Riemannian space V4 admits a representation in terms of Clebsch potentials and their derivatives. Since the usual 4−potential representation of the electromagnetic field tensor of classical electrodynamics breaks down in the presence of magnetic charges, these Clebsch potentials are treated as the field variables of an invariant variational principle. The resulting Euler–Lagrange equations determine not only a useful representation of the electromagnetic field tensor (in the presence of magnetic charges), but also give rise to Maxwell-type field equations. The associated Lagrange density defines a unique energy–momentum tensor entirely on the basis of invariance consideration. A generalized variational principle is postulated, whose Euler–Lagrange equations specify the behavior of both the electromagnetic field tensor and the metric tensor of V4. These are generalized Einstein–Maxwell equations. For the case of a spherically symmetric line-element and a static electromagnetic field an explicit solution of these equations is found which generalizes the well known Reissner–Nordström metric. In the course of the construction of this solution the magnetic charge of the central mass appears naturally as a constant of integration of the associated differential equations for the Clebsch potentials. The equations of motion of a test particle in an external electromagnetic field are also deduced from a variational principle; subject to fairly weak restrictions, the expected generalization of the classical Lorentz force emerges from this analysis." @default.
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- W2029209314 date "1977-01-01" @default.
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- W2029209314 title "Clebsch potentials in the theory of electromagnetic fields admitting electric and magnetic charge distributions" @default.
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- W2029209314 doi "https://doi.org/10.1063/1.523121" @default.
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