Understanding Stokes Theorem and is the variation of the metric a tensor?

[haushofer]

Hi, I have 2 little questions and hope to find some clarity here. It concerns some mathematics.

1) Is the variation of the metric again a tensor? I have the suspicion that it's not, because i would say that it doesn't transform like one. How can i get a sensible expression then for the covariant derivative of the variation of the metric? I need this to calculate the variation of the Riemanntensor, induced by a diffeomorphism multiplied by some test function.

2) I have the idea that I don't quite understand Stoke's theorem. Does it only apply for covariant divergences, or also for partial derivatives and/or exterior derivatives? I'm a little confused here :( I need this to rewrite the variation of an action.

Thanks in forward,

Haus.

 

[Greg Bernhardt]

@haushofer did you ever find out more about these questions?

 

[haushofer]

Hi Greg,

Yes, I did, why do you ask? I didn't recognize the podt until I saw that it's 12 years old :D

 

[Greg Bernhardt]

Hi Greg,

Yes, I did, why do you ask? I didn't recognize the podt until I saw that it's 12 years old :D

Would you be interested in writing a couple sentences on each to give insight for those guests reading this thread?