Faraday tensor vs. Maxwell-Eistein tensor

[TrickyDicky]

I'm curious about what are the similarities and differences in GR between the EM field (Faraday) tensor, a 2-form and therefore antisymmetric tensor that describes the force of the EM field in the relativistic formuation of EM, and the EM field stress-energy tensor, the part of the SET that corresponds to the EM field and that is symmetric and also of rank two.
Is the first one the Minkowskian (flat spacetime) version and the second the curved spacetime version or is this distinction too simplistic?

 

[Mentz114]

I'm curious about what are the similarities and differences in GR between the EM field (Faraday) tensor, a 2-form and therefore antisymmetric tensor that describes the force of the EM field in the relativistic formuation of EM, and the EM field stress-energy tensor, the part of the SET that corresponds to the EM field and that is symmetric and also of rank two.
Is the first one the Minkowskian (flat spacetime) version and the second the curved spacetime version or is this distinction too simplistic?

I have some difficulty parsing your post, but perhaps this is what you're asking.

The SET ( or EMT ) of the EM field is calculated from the Faraday tensor ($\mathcal{F}$) thus
$$T_{\mu\nu} = \mathcal{F}_{\mu\alpha}\mathcal{F}^\alpha_\nu - \frac{1}{4}g_{\mu\nu} \mathcal{F}^{\alpha\beta}\mathcal{F}_{\alpha\beta}$$
The metric g_μv has been used to raise indices of $\mathcal{F}$.

 

[TrickyDicky]

I have some difficulty parsing your post, but perhaps this is what you're asking.

The SET ( or EMT ) of the EM field is calculated from the Faraday tensor ($\mathcal{F}$) thus
$$T_{\mu\nu} = \mathcal{F}_{\mu\alpha}\mathcal{F}^\alpha_\nu - \frac{1}{4}g_{\mu\nu} \mathcal{F}^{\alpha\beta}\mathcal{F}_{\alpha\beta}$$
The metric g_μv has been used to raise indices of $\mathcal{F}$.

Yes, that much I can gather from the wikipedia page, but there they use the contravariant form of the SET and the Minkowski metric.