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so my question is, if for some metric, we have found (somehow) F_{μν}, and we know that:

F_{μν}=∂_{μ}A_{ν}-∂_{ν}A_{μ}, how do we find A_{ν}?

I tried solving the differential system after imposing the Lorentz gauge ∂^{μ}A_{μ}=0

but still, without some initial guess about which components of A are zero, the system cannot be solved.

Since books give often the potential A instead of F, I suppose there is a way to find it, I just can't figure it out on my own. Is there another equation to make the system determined?

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# A How to derive the EM potential from the EM tensor

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