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So apparently (wiki), the manisfestly covariant form of Maxwell's equations is dF=0 and d*F=µJ for F the Faraday 2-form and J the current 3-form. My question will probably seem silly to you but I am simply wondering how does this field affect the motion of a particle of charge q in GR? Is it just [itex]m_0\nabla_{\dot{\gamma}}\dot{\gamma}=f[/itex] for some 4-force vector field f? If so, what is the 4-force f corresponding to a Faraday 2-form F? Thanks again! :)