Electromagnetic field strength tensor- Magnetic monopoles

[Lurian]

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 $F_{ab}=A(r)(dt)_a \wedge (dr)_b+B(r)r(d\theta)_a \wedge r sin\theta (d\phi)_b$. Then, in part b, he states that a Maxwell tensor with B$\neq$0 corresponds to a magnetic monopole. How can I interpret this? I was told that the deeper reason for this is that $r(d\theta)_a \wedge r sin\theta (d\phi)_b=d^2\Omega$ is not closed but that the exterior derivative is proportional to $\delta^{(2)}(x)$. Where is the connection between these two statements?
Thank you for help

 

[Vailanor]

!The connection between these two statements is that when B is not equal to 0, the Maxwell tensor corresponds to a magnetic monopole because the exterior derivative of d^2\Omega is proportional to \delta^{(2)}(x). This means that there is a point source of magnetic field at the origin, which is indicative of a magnetic monopole. Thus, the presence of a non-zero B component in the Maxwell tensor implies the existence of a magnetic monopole.