Struggling with Einstein-Hilbert Action Syntax in Mathematica?

[Tinuviel]

Hello ,

I was trying to vary Einstein Hilbert action in Mathematica , but the syntax failed me badly.
I have derived the result by hand , but I want to present the topic with nb.file .
Nevertheless, as I said, the syntax is my major concern now.
any help will be appreciated!
thank you

 

[jedishrfu]

Perhaps if you present the math and the source code of your program someone here will see something.