Recent content by Mike Karr

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.

that that => what that

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...

Of course. Sorry to bother you with something so trivial.

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...