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Electromagnetic field strength tensor- Magnetic monopoles

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Lurian
#1
Sep13-11, 01:14 PM
P: 5
Hey!

I stumbled across this problem while reading Wald's "General Relativity", but it belongs to Electrodynamics. In problem 3 of chapter 6 one has to find the general form of a static, spherically symmetric Maxwell tensor, which is clearly [itex]F_{ab}=A(r)(dt)_a \wedge (dr)_b+B(r)r(d\theta)_a \wedge r sin\theta (d\phi)_b[/itex]. Then, in part b, he states that a Maxwell tensor with B[itex]\neq[/itex]0 corresponds to a magnetic monopole. How can I interpret this? I was told that the deeper reason for this is that [itex]r(d\theta)_a \wedge r sin\theta (d\phi)_b=d^2\Omega[/itex] is not closed but that the exterior derivative is proportional to [itex]\delta^{(2)}(x)[/itex]. Where is the connection between these two statements?
Thank you for help
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