anuttarasammyak's latest activity

Thanks. I will restate it to confirm my understanding. Here I try not to refer controversial (at least to me) tensor and concentrate on...

First of all, thanks @JimWhoKnew So in general cases which could include ##\delta g^{\mu\nu}##, do we need further information or...

I am sorry I don't understand "the same signature". If A is g itself, I think that B = A = g. A=mg, B=1/m g where m is a real number...

Going back to basics, Dirac's textbook defines a tensor as follows: $$...

I will summarize what I have written. The index-raising and -lowering relation for the metric tensor $$...

Ordinarily, ##~T^{\mu\nu}~## , ##~T_{\mu\nu}~## and ##~T^\mu{}_\nu~## are coordinate representation of the same coordinate-free object...

Thank you @JimWhoKnew for the clear and easy-to-understand explanation for the "anomaly". I have preffered to regard "new"...

Thanks. Even with this general caution, may we take it obvious that in tensor division of $$ \bar{g}_{\mu\nu} := g_{\mu\nu}+\delta...

In the world of metric tensor undertaking variation where the metric tensor is $$ \bar{g}_{\mu\nu} := g_{\mu\nu}+\delta g_{\mu\nu} $$...

@haushofer it is a good chance to learn from your comments. May I say that in GR when tensor ##A_{abc..}^{def...}## is written...

@haushofer Thanks for the teaching. $$ g_{\mu\nu}+\delta g_{\mu\nu} =( g_{\alpha\nu}+\delta g_{\alpha\nu}) (g_{\mu\beta}+\delta...

No, I don't know any case in tensors. That is one of the reasons that I think : I am afraid that you are against it in post #11...

@haushofer The equation is the application of the rule for raising and lowering the indices in use of the (varied) metric tensor to the...

Under variation of metric tensor, ##g_{\mu\nu}+\delta g_{\mu\nu} ## is a tensor but its parts ##g_{\mu\nu}## and ##\delta g_{\mu\nu} ##...

Why don't you start with the familiar case that all $$x^0,x^1,x^2,x^3$$ have dimension of length. All the metric tensor components, thus...