New to GR, having trouble with lagrangian calculation

In summary, the Euler-Lagrange equation is found using the action S = \int Ldt, where L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4, and the covariant derivative D_p is defined as D_p a^q = d_p a^q + \Gamma_p_h^q a^h. The notation may be difficult for beginners, but using LaTeX can improve readability.
  • #1
LoopQG
22
0
Find the Euler – Lagrange Equation when

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

Use [itex] g_u_v [/itex] to raise/lower indices

[itex] D_p [/itex] 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:

[itex] S = \int Ldt [/itex]

and i know the covariant derivative [itex] D_p a^q = d_p a^q + \Gamma_p_h^q a^h [/itex]I honestly have know idea where to start any help would be much appreciated.
 
Last edited:
Physics news on Phys.org
  • #2
Hi, LoopQG --

Please use LaTeX to mark up your math. Here is an example: [itex]y=ax^2[/itex]. 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
 
  • #3
Thanks Ben,

I'm new to physics forum didn't know you could do that, appreciate the help!
 
  • #4
Try the following Latex, you can quote my post to see the code...

[tex]
\nabla_{p}
[/tex]

[tex]
\Gamma^{q}{}_{ph}
[/tex]

[tex]
\partial_{p}
[/tex]
 
  • #5
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
 

1. What is a Lagrangian calculation?

A Lagrangian calculation is a mathematical method used in the study of physics, particularly in the field of general relativity. It involves calculating the motion of a system by minimizing the action, which is a mathematical quantity that represents the total energy of the system.

2. Why is Lagrangian calculation important in general relativity?

In general relativity, the equations of motion are difficult to solve using traditional methods. Lagrangian calculation provides a more elegant and efficient way to solve these equations and understand the behavior of objects in space and time.

3. What are some common challenges in performing Lagrangian calculations?

Some common challenges in performing Lagrangian calculations include dealing with complex and non-linear equations, determining the appropriate boundary conditions, and accounting for all relevant variables and parameters.

4. How can I improve my Lagrangian calculations?

To improve your Lagrangian calculations, it is important to have a strong understanding of the underlying principles and mathematical concepts. It can also be helpful to use software or computer programs specifically designed for Lagrangian calculations.

5. Are there any resources available to help with Lagrangian calculations?

Yes, there are many resources available for those struggling with Lagrangian calculations. These include textbooks, online tutorials, and forums where you can ask for help from experts and fellow scientists.

Similar threads

  • Special and General Relativity
Replies
7
Views
804
  • Special and General Relativity
Replies
18
Views
2K
  • Special and General Relativity
Replies
7
Views
998
Replies
25
Views
1K
Replies
19
Views
1K
  • Special and General Relativity
Replies
10
Views
2K
  • Special and General Relativity
Replies
20
Views
1K
  • Special and General Relativity
Replies
6
Views
3K
Replies
3
Views
858
  • Special and General Relativity
Replies
4
Views
1K
Back
Top