Recent content by gnieddu

Thanks. I thought I'd have to have some expression for ##dz^2## in order to account for the fact that the clock's z coordinate is changing in time (and not uniformly due to the accelerated motion), but I not I get yor point.

Hi TSny, thanks for your feedback (and apologies for my late reply). You're right about the typo in my formula: the expression under the integral should be square-root-ed. Regarding the meaning of "GR only", my assumption is that I should compute the time dilation using only the GR metric vs...

The non-moving clock will see the other one move upwards and land as predicted by Newton's laws, so using the equation ##z=v_0t-\frac{1}{2}gt^2##, and assuming the moving clock starts at ##t=0##, it will land at ##t=\frac{2v_0}{g}##. Now, using SR only, and the Minkowski metric (with signature...

fresh_42 & Oxvillian, many thanks for your discussion, which helps me to gain different angles and views on this subject! I've also read fresh_42's insight, which I'm finding very useful. If, as you say, SU(n) representations were always noted using a triplet ##(SU(n),V,\phi)## that would...

Hi, thanks for your reply, and apologies for my late response (I can only work on this in my spare time). So, I followed your instructions, and calculated the second term, which should be: $$\begin{pmatrix}\beta \\ \bar\alpha\end{pmatrix} \otimes \begin{pmatrix}\alpha \\...

Homework Statement Hi, I'm trying to self-study quantum mechanics, with a special interest for the group-theoretical aspect of it. I found in the internet some lecture notes from Professor Woit that I fouund interesting, so I decided to use them as my guide. Unfortunately I'm now stuck at a...

That's unlikely: in the same section, the text notes that, at the border of \hat{M}, where \Omega=0, \hat{\nabla}_a\Omega\hat{\nabla}^a\Omega = 0. This makes sense only if you start from \hat{\nabla}_a\Omega\hat{\nabla}^a\Omega = \Omega^2. Thanks for the suggestion, anyway...

Homework Statement This is not really part of some homework, but I'd rather post it here than annoy other people on the more general threads. I'm trying to self study the topic of asymptotic flatness related to General Relativity. The textbook I'm using tries to explain the concept by...

Thanks!

Hi, I'm struggling to grasp the physical reason behind the fact that, in a curved spacetime, a change of metric implies, in general, a change of connection, i.e. if I have two metrics g_{ab} and \hat{g}_{ab}, in general \nabla_a \neq \hat{\nabla}_a. Besides this, is there any relationship...

Hi George, thanks very much for the clear explanation! That clarified my doubts. Best regards Gianni

Hi George, while thinking about the issue introduced by Altabeth, there's another question that your reply above suggests. In the chain of equalities, you deal with g_{cb} as if it were a constant, and so you can take it out of the scope of the nabla operator. This is what I normally do as...

I think I got it. If I "multiply" by u_b as you suggest, I'm still able to get rid of the two \dot{p} terms and the equation reduces to: (\varrho+p)u^au_b\nabla_au^b+u^a\nabla_a\varrho+(\varrho+p)\nabla_au^a=0 Now the first term is zero, since...

Hi George, just trying to follow you here. So since, as you say u^a \nabla_a is equivalent to an overdot, applying it to 1 = u_b u^b should give: 0 = \dot{u}_bu^b + u_b\dot{u}^b but it does not lead me too far. I was also trying to follow your previous hint (i.e. to use the fact that...

Hi, I'm trying to work out the logic behind a statement I found in the GR book I'm currently studying. It says that from the conservation equation \nabla_aT^{ab}=0, one could deduce the following two equations: (\varrho+p)\dot{u}^a = \nabla^ap - u^a\dot{p} \dot{\varrho} +...