Table of Connection Coefficients

  • Thread starter glamotte7
  • Start date
  • #1
glamotte7
19
0
Hello,

I'm trying to find a table of basic connection coefficients. My GREAT desire is to find a table that includes the metric, connection coeffs, Riemann tensor, Ricci tensor and Ricci scalar for NORDSTROM's 1913 scalar theory of gravity.

Does anyone know an online source of this info?

glamotte7
 

Answers and Replies

  • #2
Matterwave
Science Advisor
Gold Member
3,966
327
Since Nordstrom's theory is a scalar theory, wouldn't it lack these tensors? That's just my thought, but I don't know much about his theory.
 
  • #3
Ben Niehoff
Science Advisor
Gold Member
1,883
168
Nordstrom's theory is still a geometric theory of gravity. The metric is always a conformal factor times Minkowski space:

[tex]ds^2 = e^{2 \phi} \, (-dt^2 + dx^2 + dy^2 + dz^2)[/tex]

It is very easy to compute the Christoffel symbols and curvature tensors for this metric. Why don't you try it!
 
  • #4
glamotte7
19
0
For small ∅ this would be 1 + (2∅), correct?

What does the word conformal factor mean? Why is it advantageous to use an exponential as opposed to some other function? I've seen other important GR equations solved beginning with an arbitrary exponential. Why is this the best approach for a solution?

Lastly, I'm new here. How do you type math expressions like dx^2, etc?
 
  • #5
glamotte7
19
0
Also, in Nordstrom's scalar theory, can't the scalar conformal factor be multiplied in an unequal fashion times -dt,dx,dy and dz? For example, can't dy and dz remain multiplied by 1 rather than multiplied by the factor, which in this case the factor would only affect dt and dx?
 
  • #6
Ben Niehoff
Science Advisor
Gold Member
1,883
168
Why is it advantageous to use an exponential as opposed to some other function?

The exponential is just to remind us that it has to be a positive number. Set [itex]\phi = \log u[/itex] if you want, it doesn't matter.

Also, in Nordstrom's scalar theory, can't the scalar conformal factor be multiplied in an unequal fashion times -dt,dx,dy and dz?

No.
 
  • #7
glamotte7
19
0
Are you aware of a basic review article or reference on Nordstrom's scalar theory, accessible online?
 

Suggested for: Table of Connection Coefficients

  • Last Post
Replies
34
Views
2K
Replies
14
Views
4K
Replies
13
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
954
  • Last Post
Replies
2
Views
784
  • Last Post
Replies
6
Views
2K
Replies
2
Views
981
Top