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Hi, I am having problems in constructing a stress-energy tensor representing a constant magnetic field Bz in the [itex]\hat{z}[/itex] direction. The coordinate system is a cylindric {t,r,z,[itex]\varphi[/itex]}. The metric signature is (+,-,-,-).

I ended with the following mixed stress-energy tensor:

Is this correct?

How to properly construc this general magnetic field stress-energy tensor that exists without sources?

Thank you,

Coleman

I ended with the following mixed stress-energy tensor:

Is this correct?

How to properly construc this general magnetic field stress-energy tensor that exists without sources?

Thank you,

Coleman