- Summary
- Formula for the Electromagnetic Stress Energy Tensor

I am trying to find the correct formula for the electromagnetic stress energy tensor with the sign convention of (-, +, +, +).

Is it (from Ben Cromwell at Fullerton College):

$$T^{\mu \nu} = \frac{1}{\mu_0}(F^{\mu \alpha}F^{\nu}{}_{\alpha} - \frac{1}{4}g^{\mu\nu}F_{\alpha\beta}F^{\alpha \beta})$$

but I have also seen it with a negative sign:

$$T^{\mu \nu} = -\frac{1}{\mu_0}(F^{\mu \alpha}F^{\nu}{}_{\alpha} - \frac{1}{4}g^{\mu\nu}F_{\alpha\beta}F^{\alpha \beta})$$

Which is the correct formula? Also for flat space-time ##g^{\mu\nu} = \eta^{\mu\nu}## and for curved space-time ##g^{\mu\nu}## is whatever metric being used for the curved space-time situation one is working in, correct?

Thanks.

Is it (from Ben Cromwell at Fullerton College):

$$T^{\mu \nu} = \frac{1}{\mu_0}(F^{\mu \alpha}F^{\nu}{}_{\alpha} - \frac{1}{4}g^{\mu\nu}F_{\alpha\beta}F^{\alpha \beta})$$

but I have also seen it with a negative sign:

$$T^{\mu \nu} = -\frac{1}{\mu_0}(F^{\mu \alpha}F^{\nu}{}_{\alpha} - \frac{1}{4}g^{\mu\nu}F_{\alpha\beta}F^{\alpha \beta})$$

Which is the correct formula? Also for flat space-time ##g^{\mu\nu} = \eta^{\mu\nu}## and for curved space-time ##g^{\mu\nu}## is whatever metric being used for the curved space-time situation one is working in, correct?

Thanks.