Variation of Metrics: Formula & Proof Explained

[mertcan]

hi, When I read variation of metric, I bumped into a unfamiliar formulation for me. You can see the formula in my attachment. I can not understand where this comes from. Could you provide me with the proof of that formula?

By the way, you can go to this link to look at from which the attachment is quoted ( http://www.if.nu.ac.th/sites/default/files/bin/BS_chakkrit.pdf ) page 27. Thanks in advance...

 

[Mr-R]

Hi mertcan

https://preposterousuniverse.com/wp-content/uploads/grnotes-four.pdf have a look at page 115. Near the bottom of the page.