New to GR, having trouble with lagrangian calculation

[LoopQG]

Find the Euler – Lagrange Equation when

L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4

Use g_u_v to raise/lower indices

D_p is the covariant derivative

I am very new at this notation and am having a lot of trouble getting anywhere with this.

I know I have to take the action:

S = \int Ldt

and i know the covariant derivative D_p a^q = d_p a^q + \Gamma_p_h^q a^hI honestly have know idea where to start any help would be much appreciated.

 

[bcrowell]

Hi, LoopQG --

Please use LaTeX to mark up your math. Here is an example: y=ax^2. To see how this example is done, click the QUOTE button on my post. You can then LaTeX-ify your original post by going back and editing it.

-Ben

 

[LoopQG]

Thanks Ben,

I'm new to physics forum didn't know you could do that, appreciate the help!

 

[pervect]

Try the following Latex, you can quote my post to see the code...

<br /> \nabla_{p}<br />

<br /> \Gamma^{q}{}_{ph}<br />

<br /> \partial_{p}<br />

 

[bcrowell]

The good news is that your post is now more readable and likely to attract helpful answers. The bad news is that I don't know the answer. Sorry, but maybe I'll learn something myself by watching for good answers from others:-)

-Ben