#### PeterDonis

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Continue reading...In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going to build on what we saw in the first article to show what Maxwell’s Equations in a static, spherically symmetric spacetime look like.

The electromagnetic field tensor is given in general by

[tex]F_{ab} = \partial_b A_a – \partial_a A_b[/tex]

where [itex]A_a[/itex] is the electromagnetic 4-potential.

In covariant form, Maxwell’s Equations in general are:

[tex]\partial_c F_{ab} + \partial_b F_{ca} + \partial_a F_{bc} = 0[/tex]

[tex]\nabla_a F^{ab} = \partial_a F^{ab} + \Gamma^a{}_{ac} F^{cb} = 4 \pi j^b[/tex]

The first equation is an identity given the definition of ##F_{ab}##; the second equation links the EM field to its source, the charge-current 4-vector ##j^b##, and is the one we will be focusing on here...