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4:07 AM
While deriving vanishing of covariant derivative of metric tensor,Schutz says in pg 132-"But now this equation is a tensor equation, so its validity in one coordinate system implies its validity in all",how far is this true?

I mean $g_{\mu\nu}=\eta_{\mu\nu}$ for Minkowskian flat spacetime,but it isn't possibly true for all spacetime(globally)?

I have seen a lot of usage of this fact.Where can I find a formal proof of the same?
And how does it not contradict with what I said above?
 
 
5 hours later…
9:08 AM
@ManasDogra A spacetime is something different from a coordinate system.
The equation $g_{\mu\nu}=\eta_{\mu\nu}$ is true in all coordinate systems on Minkowski space.
It's not true on a different spacetime, but that's not what Schutz is saying.
 
 
4 hours later…
12:42 PM
Could someone answer my question
 
May 26 at 15:44, by ACuriousMind
@satan29 Please don't post your questions here directly after you asked them; interested people watch the main site anyway, and if everyone did it, the room would be flooded with new questions.
 
nice to see i am mentioned repeatedly in hbar :)
 
Could someone tell me what all maths subjects are needed to study Gr. I was starting GR and I did not understand the matrices and all , Could someone tell me what all maths topics r necessary
 
@satan29 oh sorry, did that ping you?
 
no no
i happened to be online...
all the times you have used this message to discourage users from posting questions XD
 
12:57 PM
I was briefly afraid that I had pinged you every time :P
@Naruto If the matrices are the problem, you should probably start with special relativity and linear algebra first
 
Thanks Acuriousmind
 
> Your definition of work needs a little...work, it only works for forces which are constant...
It worked well but I guess that's a lot of work :-)
 
1:52 PM
@satan29 ‘love your avatar.
you must be looking for a career as university faculty.
 
Can we use the differential equation adx=vdv for calculating freefall velocity in case of large height?
 
2:26 PM
There was a conversation a while ago where Slereah mentioned a name for some set of admissible functions and I can't for the life of my remember what it was, I think it was in the context of functions on a manifold
It was something like "Jordan functions", where the first word is someone's name
they all satisfied some condition, like continuity or differentiability or something like that, but I can't remember what
 
That's hard to say without a bit more context of what the purpose of these functions is :P
Perhaps Schwartz functions? It's the space of test functions for tempered distributions, and they're the kind of functions that "fall off towards infinity sufficiently fast" you usually want for physical fields.
 
yess that's what it was, Schwartz functions
thank you, I can live peacefully now
 
@ZeroTheHero XDDD
nah mate I am not even in college yet
 
 
2 hours later…
4:25 PM
information theory is an discipline of technology or engineering rather than sciences. No wonder I am not versed with it.
 
 
1 hour later…
5:49 PM
Is probability space in mathematics equivalent completely to ensemble in physics?
 

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