Recent content by Ryomega

Hello! Thank you for the quick reply! The equation you have mentioned, the only equation I am aware of for relating christoffel symbols to the metric is: \GammaLab = \frac{1}{2} gLc (gac;b + gcb;a - gba;c) I'm having a hard time understanding the indices, thus just how to use this...

Homework Statement Consider metric ds2 = dx2 + x3 dy2 for 2D space. Calculate all non-zero christoffel symbols of metric. Homework Equations \Gammajik = \partialei / \partial xk \times ej The Attempt at a Solution Christoffel symbols, by definition, takes the partial of each...

That would give me: 2Ui\frac{dU^i}{d\tau} = 0 And that would be the proof. The identity Ui\frac{dU^i}{ds} = 0 Similarly, identity Ui\frac{dU^i}{d\tau} would be zero

Alright, it took me a while but here's what I got: UiUi = 1 \frac{d}{d\tau} (UiUi) = 0 chain rule:\frac{d}{dx} f(x)g(x) = f(x)g'(x)+ f'(x) g(x) Ui\frac{dU^i}{d\tau} + \frac{dU_i}{d\tau} Ui = 0 [EQ1] Raising and lowering indices: Ui = gkiUk Ui = gniUn Making these...

Ah yes, I see where I went wrong on [eq 1]. I was coming from the convention that: Vector U = Uaea where ea can represent [i,j,k] [x,y,z] and in case of tangents, it can represent partial derivatives of correspondent components. I forgot to include that, now a sum is implied and [eq 1] would...

Ok, I've resolved some issues with my understanding of index notations: [SIZE="3"]Ui = \frac{dx^i}{d\tau} [eq 1] Such that writing out component form: [SIZE="3"]Ui = \frac{dx^0}{d\tau} + \frac{dx^1}{d\tau} + \frac{dx^2}{d\tau} + \frac{dx^3}{d\tau} Where U1,2,3 would...

I'd like to take a moment while I'm struggling through this problem to thank you guys for helping and guiding me. Thank you so much!

oh dear kronicker delta function! I'll have to tackle this tomorrow, it's bed time. Thank you very much for helping me! I'll be back with...something

After searching, I haven't been able to find product rule for tensor calculus (I did find dot product but has no examples with lower index multiplied by higher index. As previously mentioned I'm unaware of the meaning of U_i. I know that U_i and U^i are related by the metric. Is this the sort...

Yes, I do have to prove that the latter equation you have mentioned is = 0. Getting from eq 1 to eq 2 would imply taking the \frac{d}{d\tau} from eq 1. This would give me: \frac{dU_i}{d\tau} \frac{dU^i}{d\tau} = \frac{dc}{d\tau} Letting i = 0, U0 = ct = c\gamma\tau \frac{dU_0}{d\tau}...

I'm sorry, but I'm afraid I'll need a little bit more than that to go on. I see what you meant with myself not recognising a four-vector earlier. This is what's floating around in my head at the minute: I know that: UiUi = -c2 I also know that: Ui \frac{dU^i}{d\tau} = 0 let...

Yes the contents of the wiki page is what is being covered in class at the moment. I am working to make them very familiar, but as you can see, I have a few kinks I need to work out. Regarding the contradicting sentences, yes, there was a confusion with tensor ranks (thank you for point that...

Oh and I'm interpreting Ui to be some scalar since its rank is 1

UiUi would imply a summation. U1*\frac{dU^1}{d\tau}+U2*\frac{dU^2}{d\tau}... Since Ui is defined as a four-vector in this example, and Ui is present (i once raised once subbed) I imagined that this expression implies a summation. Do I have everything completely wrong here? Thanks for...

Homework Statement Show that Ui \frac{dU^i}{d\tau} = 0 Homework Equations Raising Indices: Ui = gkiUi = Ui where gk is a dummy index The Attempt at a Solution I'm interpreting this question to mean a scalar multiplying each component of a four vector = 0. Also, since the same...