anuttarasammyak's latest activity

$$\bar{g}_{\mu\nu} - g_{\mu\nu} = \delta g _{\mu\nu} = - \delta \bar{g}_{\mu\nu} $$ ##\bar{g}_{\mu\nu}## is a tensor in the world where...

I agree that index raise- lower operation should be done using one same, old or new, metric for all the indexes of all the entities in...

My bad. I withdraw it.

To me the point is two metrics: original and varied. In varied metric world what kind of things or relations remain and what does not ?

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...