Hi all, I'm fairly new to GR, and I'm also somewhat new to tensors as well. I'm looking for some detailed explaination of a tensor, as I want to begin studying GR mathematically. I watched a video that was posted on PF not too long ago that was pretty good. I'm having trouble remembering who it...
The Faraday Tensor is given by:
Consider the following outer product with the 4-potential:
The Faraday Tensor is related to the 4-potential:
F^{mn} = \Box^{m} A^n - \Box^n A^m
For example, ## F^{01} = -\frac{1}{c} \frac{\partial A^x}{\partial t} - \frac{1}{c}\frac{\partial...
Hello,
I am working through the MIT OCW courses 8.01 and 8.012. At my university we already learned about tensors in the first mechanics course but I don't really understand them completely.
Therefore I am searching for some MIT OCW course that covers tensors.
I'd be glad at any help...
1. Homework Statement
Half disk, radius R, mass m. I need the inertia tensor about the center of mass and then find the Principal moments of inertia about another coordinate system. Struggling with the product of inertia...
1. Homework Statement
A tensor and vector have components Tαβγ, and vα respectively in a coordinate system xμ. There is another coordinate system x'μ. Show that Tαβγvβ = Tαβγvβ
2. Homework Equations
umm not sure...
∇αvβ = ∂vβ/∂xα - Γγαβvγ
3. The Attempt at a Solution
Tαβγvβ =...
Hello everyone!
Even though I have done substantial tensor calculus, I still don't get one thing. Probably I am being naive or even stupid here, but consider
$$R_{\mu\nu} = 0$$.
If I expand the Ricci tensor, I get
$$g^{\sigma\rho} R_{\sigma\mu\rho\nu} = 0$$.
Which, in normal algebra, should...
Hello! I'd appreciate any help or pokes in the right direction.
1. Homework Statement
Show that a co-tensor of rank 2, ##T_{\mu\nu}##, is obtained from the tensor of rank 2 ##T^{\mu\nu}## by using a metric to lower the indices:
$$T_{\mu\nu} = g_{\mu\alpha}g_{\nu\beta}T^{\alpha\beta}$$
2...