PeterDonis, thank you! It's nice when the problem is easier than it seems. And especially for the general tip about "weird quirks." I'll be on the lookout.
Well, I have been inducted into the joys of electromagnetic units, and I have certainly been confused for a while. However, if I ignore all that and use only formulas in MTW, I can derive:
## \nabla \cdot \frac{E \times B}{4 \pi} = - \frac{\partial}{\partial t}(\frac{E^2 + B^2}{8 \pi}) - E...
My physics background is weak. My search found lots of ## E \times B ## and ## E^2 + B^2##, often associated with ## \mu_0 ## and ## \epsilon_0 ##, but never divided by ## 4 \pi ## and ## 8 \pi ##, respectively. Could someone provide a reference? Or a derivation? Thanks.
ergospherical, thanks for your answer. What I was doing wrong was using the wrong components in ##F^{\alpha\beta} ##---I swapped the 0th row and 0th column. But your answer is much more clever, using formulas for ##E_i## and especially for ##B_i## that I would never have thought of. Also, I...
Sorry, I got unconfused too quickly. I don't get the correct answer for ## T^{00} ##. Let's look at the two terms of equation 5.22. The last one is simple, I think:
## - \frac{1}{4} \eta^{\mu\nu} F_{\alpha\beta} F^{\alpha\beta}
= - \frac{1}{4} \eta^{\mu\nu} 2(E_x^2 + E_y^2 + E_z^2 + B_x^2...
I am a beginner in GR, working my through Gravitation by the above authors. If there is a better place to ask this question, please let me know.
I understand (from section 5.7) that the stress-energy tensor is symmetric, and from equation 5.23 (p. 141), it is explicitly symmetric. But...