Recent content by mjordan2nd

Thank you for pointing this out. I have a tendency to miss these kind of connections and get lost in the heap of algebra, especially when learning something new.

Never mind. I now see that my formula for the Lie derivative is wrong. The minuses should be pluses.

In one of the lectures I was watching it was stated without proof that the Schwarzschild metric is spherically symmetric. I thought it would be a good exercise in getting acquainted with the machinery of GR to show this for at least one of the vector fields in the algebra. The Schwarzschild...

I googled Bishop and Goldberg and came across this post and thought, wow, this guy has the exact same issues I did. It's remarkable, he's expressing this in almost the same way I would. I then looked at who wrote this post and realized it was me. Anyway, if anyone else does have the same issue...

Let me rephrase: is there experimental evidence that a particle with 0 rest-mass by itself will warp spacetime?

Is there any experimental evidence that pure energy (massless) can curve spacetime?

The problem is that I don't know how to isolate Q in my equations above when trying to look at the dust energy-momentum tensor.

Homework Statement For a system of discrete point particles the energy momentum takes the form T_{\mu \nu} = \sum_a \frac{p_\mu^{(a)}p_\nu^{(a)}}{p^{0(a)}} \delta^{(3)}(\vec{x}-\vec{x}^{(a)}), where the index a labels the different particles. Show that, for a dense collection of particles...

I'm trying to show that \partial_\mu T^{\mu \nu}=0 for T^{\mu \nu}=F^{\mu \lambda}F^\nu_{\; \lambda} - \frac{1}{4} \eta^{\mu \nu} F^{\lambda \sigma}F_{\lambda \sigma}, with the help of the electromagnetic equations of motion (no currents): \partial_\mu F^{\mu \nu}=0, \partial_\mu F_{\nu...

I'm not entirely sure. From what I recall, when we derive the energy-momentum tensor from the Lagrangian it's derived as a mixed tensor as in 1.41 here: http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf. At the same time, I know a lot of identities regarding the tensor and equations using the...

Correct.

Sorry, should have read your post more carefully. Eta is what the flat spacetime metric is typically denoted by. Simply replace it with g and it's consistent with your notation. You can raise the index on the second part of your problem in the same way.

F^{\alpha \beta} = \eta^{\mu \alpha} \eta^{\nu \beta} F_{\mu \nu} \frac{\partial}{\partial(\partial_{\sigma}A_{\rho})} F^{\alpha\beta}= \eta^{\mu \alpha} \eta^{\nu \beta} \frac{\partial}{\partial(\partial_{\sigma}A_{\rho})} F_{\mu \nu}

For the first part you need to lower the indices as you stated and use the product rule.

Ahh, I forgot to write a factor up there. Ahh, I forgot to write a factor up there. Is it better now?