Tutorial on the Christoffel equation used in relativity

Could someone give me a brief tutorial on the Christoffel equation used in relativity please
 
Thanks Ambit thats what I was talking abuot
 
916
0
Can somebody confirm if the Christoffel symbols of the first kind are tensors? I thought that it was the case, but I've found the notes of Stefan Waner were he assures that they are not
http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/Sec8.html [Broken]
 
Last edited by a moderator:
837
1
It's kind of a matter of definition. It has been traditional to say that the Christoffel symbols are not tensors, because they don't transform like tensors. If you're of the Wald school, however, you will say that the Christoffel symbols are tensors; it's just that there is a different Christoffel tensor for each coordinate system.

In more detail: the Christoffel symbols are defined as the difference between the Levi-Civita connection and a fiducial connection given by the partial derivatives in some coordinate system, ∇ = ∂ + Γ. The difference of two connections is a connection. However, the fiducial connection ∂ depends on the coordinate system (since it's the partial derivatives of some coordinates), so the Christoffel symbols do too. For this reason, they don't obey the ordinary transformation law for tensors, because that assumes you are transforming the components of a single tensor field; with Christoffel symbols, if you change the coordinates, you also change which tensor field you're working with.
 

Related Threads for: Tutorial on the Christoffel equation used in relativity

Replies
0
Views
8K
Replies
1
Views
1K
Replies
1
Views
2K
Replies
15
Views
726
Replies
1
Views
3K
Replies
3
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top