Table of Connection Coefficients

In summary, Nordstrom's theory is a geometric theory of gravity that lacks the familiar Ricci tensors. However, it is very easy to compute Christoffel symbols and curvature tensors for this metric, and typing math expressions like dx^2, etc. is easy with the help of exponentials.
  • #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
 
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  • #2
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
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
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
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
glamotte7 said:
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.

glamotte7 said:
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
Are you aware of a basic review article or reference on Nordstrom's scalar theory, accessible online?
 

1. What is a Table of Connection Coefficients?

A Table of Connection Coefficients is a statistical tool used in social network analysis to measure the strength of relationships between individuals or entities in a network. It displays a matrix of values representing the degree of connection between each pair of nodes in the network.

2. How is a Table of Connection Coefficients created?

A Table of Connection Coefficients is created by first identifying the nodes (individuals or entities) in the network and then calculating the strength of the connections between each pair of nodes. This can be done using various methods, such as counting the number of direct connections or measuring the frequency and intensity of interactions between nodes.

3. What is the purpose of a Table of Connection Coefficients?

The purpose of a Table of Connection Coefficients is to provide a visual representation of the relationships and connections within a network. This can help researchers understand the overall structure of the network and identify key individuals or entities that play important roles in the network.

4. How are the values in a Table of Connection Coefficients interpreted?

The values in a Table of Connection Coefficients typically range from 0 to 1, with higher values indicating stronger connections between nodes. A value of 0 means there is no connection between the two nodes, while a value of 1 represents a perfect connection. Values in between indicate varying degrees of connection strength.

5. What are some limitations of using a Table of Connection Coefficients?

One limitation of using a Table of Connection Coefficients is that it only measures the strength of connections between nodes and does not consider the direction or quality of those connections. Additionally, it may not capture the complexity of real-world relationships and may oversimplify the connections within a network.

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