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Jay21
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- TL;DR 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.