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I am trying to develope magnetic terms in the Minkowski field tensor, based on an electron model positing circular currents and thus [tex]A_{\phi}[/tex]. It is easy enough to decompose this into [tex]A_{x,y}[/tex] and construct the tensor in a Cartesian basis, but essentially my study requires spherical coordinates because my goal is not just to reproduct Maxwell's equations, but to put this magnetic field into the Reissner-Nordstrom solution in spheric coordinates. No reference I've yet found deals with this: the circular vector potential manifests [tex]B_r [/tex] and [tex]B_\theta [/tex]. I need to be sure of the three expressions of the Minkowski form since you need covariant, contravariant, and mixed to build up the RHS of the Einstein equations, the stress-energy tensor. I have already accomplished this with the inhomogeneous electric field, which though not a point source, worked through the usual radial field solution without such difficulty. This problem is represented with only an [tex]E_r[/tex] so nothing usually is shown about the magnetic off-diagonal terms needed here. It is not so hard to effect a rotation of the orthogonal vector basis, as per spheric coordinates, but the formalism is not easy through the rest of this problem. The spheric coord. transform is like a rotation and a scale matrix with diagonal elements of [tex]<1,r,rsin\theta>[/tex]. This is like the square root of the metric [tex]g_{ab}[/tex] usually spoken of. . . . . . . .Part of this issue revolves around getting the expressions for

*CURL*straight, in the spheric coords.
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