= Curved-spacetime electromagnetic potential wave equation
{title2=$\Box A_\nu-R^\alpha{}_\nu A_\alpha=-\mu_0J_\nu$}
With convention $\nabla^\mu F_{\mu\nu}=-\mu_0J_\nu$, write the <electromagnetic field tensor> as $F_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu$. Commuting the contracted <covariant derivatives> gives $\nabla^\mu\nabla_\nu A_\mu=\nabla_\nu(\nabla^\mu A_\mu)+R^\alpha{}_\nu A_\alpha$. The <Lorenz gauge condition> removes the gradient-of-divergence term, leaving the displayed <wave equation> for a <covector field>. A locally inertial coordinate system does not eliminate the <Ricci tensor> term.
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