The result at 4:39 for the variation of the Christoffel symbols contains a typographical error. The covariant derivatives should act on the variation of the metric, not on the metric itself. This error persists throughout the video.
Wow, very clear.!! I didn't use to understand the total derivative term from the variation of Ricci tensor ever. Thanks !!. I could've not made it without you.!
okay, so first let me state the definition for the variational operator. This definition is referenced from Haim Brezis - Functional Analysis. Let H be a Hilbert space, let A ⊆ H and M is a subspace of H. Consider a functional J : A ⟶ IR, u ⟼ J[u]. For v ∈ M and u ∈ A, We define the Gateaux derivative of J at u in direction v as the following limit when ε → 0 lim ( J[u+εv] - J[u] )/ε =: δJ/δv [u] So basically, the Hilbert action S_EH is a functional. So what is the Hilbert space H, the subset A and the subspace M in this context ?
Preferably in the hand writing style video. The computer generated videos are super cool to look at, but they go really quick and are more difficult to follow.
Many years ago a man named Einstein discovered, partly by guessing, a now famous equation (no, not e equals mc squared) and a few years later someone else came along and said that this same famous equation, discovered by Einstein, could actually be derived from an action principle if you start with the right Lagrangian. Well, this is that. Now you know. Funny, I asked the same question about two years ago!
The result at 4:39 for the variation of the Christoffel symbols contains a typographical error. The covariant derivatives should act on the variation of the metric, not on the metric itself. This error persists throughout the video.
is theses differential foms usefull like biannchi identity?
Wow, very clear.!! I didn't use to understand the total derivative term from the variation of Ricci tensor ever. Thanks !!. I could've not made it without you.!
I've watched this video so many times to review the subject. Thank you for making it!
My only hope is that one day, after watching several hundreds of these videos, I may understand just one of them.
It's a challenging subject, for sure. Good luck!
Gently's Channel Watch eigenchris’s tensor algebra and calc video. You’ll get it then.
you should study from the beginning. osmosis don´t work.
so clear and well organized, great work!
Thanks yong!
Thank you for the explanation! The style of the video is very clear
Thank you Akushu...
At 5:39~5:40, when Riemann tesor is contracted with g_(μ)^(ν) to make Ricci tensor, isn't "g_(μ)^(ν)" term also subject to variation?
Very clear vudeo! It really helped me. But I had a question. How we define a boundary term? Thank you for your time!
Now I can understand moon orbiting behavior
Could you give me the bibliographical references that were used in this video?
thanks for the clear explanation
okay, so first let me state the definition for the variational operator. This definition is referenced from Haim Brezis - Functional Analysis.
Let H be a Hilbert space, let A ⊆ H and M is a subspace of H. Consider a functional J : A ⟶ IR, u ⟼ J[u].
For v ∈ M and u ∈ A, We define the Gateaux derivative of J at u in direction v as the following limit when ε → 0
lim ( J[u+εv] - J[u] )/ε =: δJ/δv [u]
So basically, the Hilbert action S_EH is a functional. So what is the Hilbert space H, the subset A and the subspace M in this context ?
Very well done
Can you do a video about the Lagrangian formulation in general relativity?
Preferably in the hand writing style video. The computer generated videos are super cool to look at, but they go really quick and are more difficult to follow.
I would love to cover that topic. It's on my list of things to do, I just need to find the time...
Excuse me sir. What happen if take variation of Ricci Tensor Rab with respect to variation of inverse metric tensor gab?
If you did that you would defeat the strategy which is to get all three in terms of delta g ab downstairs. You would be in a different movie, dude.
what is the definition of "d^4" ?
Noticed that you changed from hand writing. Are you going to stick with this new type from now on?
I haven't decided. The computer generated video is very labor intensive to create. So we'll see...
General relativity credit to Hilbert
Okay but you barely explained going frok one step to another
10 sekúnd = 100 rokov
ANO
what the fuck is this?
Finally, i see response that makes sense😂
Many years ago a man named Einstein discovered, partly by guessing, a now famous equation (no, not e equals mc squared) and a few years later someone else came along and said that this same famous equation, discovered by Einstein, could actually be derived from an action principle if you start with the right Lagrangian. Well, this is that. Now you know. Funny, I asked the same question about two years ago!