Can one show that strict charge conservation ##\nabla_{a}J^{a} = 0## follows directly from ##\nabla_{a}F^{ab} = 4\pi J^{b}## alone?(adsbygoogle = window.adsbygoogle || []).push({});

Also, how does ##d^{\star}F = 4\pi ^{\star}J## follow directly from that same equation where ##\star## is the Hodge dual operator?

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# Maxwell's Equations in Curved Space-time

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