Covariant divergence question from Landau and Lifshitz

[maverick280857]

Hi everyone,

I'm trying to work through section 86 of Landau and Lifgarbagez volume 2 (The Classical Theory of Fields).

Basically, I am unable to get equation (86.6) from equations (86.4) and (86.5). I've detailed my working/question in the attached jpg file. I would appreciate any inputs.

Thanks in advance!
Cheers
Vivek

 

[clamtrox]

I bet they've calculated $$\partial \sqrt{-g} / \partial x^{\mu}$$ somewhere.

 

[George Jones]

Take a look at section 1.7 in Eric Poisson's excellent notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

Better yet, see if your library has a copy of the excellent book, A Relativist's Toolkit: The Mathematics of Black Hole Mechanics, into which the notes evolved.

 

[maverick280857]

George, thanks a lot for this very useful link! Unfortunately, my school library does not have this book.

 

[lalbatros]

Try this:

http://books.google.com/books?id=v-...q=A+Relativist's+Toolkit#v=onepage&q=&f=false

Maybe you are lucky with the pages available there.
You could also have a look for a preview on Amazon.