Where can I find a list of Christoffel Symbols for Various Metrics?

In summary, the conversation discusses the search for a list of Christoffel Symbols for various metrics, including famous ones like Schwarzschild and Robertson-Walker. The conversation also mentions the use of computer programs like Maple to calculate the symbols instead of doing it by hand, which can be tedious and confusing. It is recommended to do it by hand once or twice for understanding, but relying on computer programs for further calculations.
  • #1
Chaosmarch
7
0
Does anyone know where I can find a list of Christoffel Symbols for various metrics? Metrics of general forms, as well as famous ones like Schwarzschild and Robertson-Walker? Yes, I can calculate them all if I really need to, but it's pretty tedious.
 
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  • #2
Maple + GRTensor package.
 
  • #4
Thanks, that's a very useful resource, though I was looking for a list, analogous to a Table of Integrals.
 
  • #5
Any such list would be hopelessly confusing, b/c you might get different forms for the symbols depending on the coordinate system/notation you use, even for identical physical metrics.

Hence the computer programs, like Maple that do it for you (rather than tediously going through it by hand) for whatever notation and coordinates you might want to use.

In general I recommend doing it once or twice by hand (usually its a homework problem to compute the Christoffel symbols, Ricci tensor and Riemann tensor for say the Schwarzschild metric) and then never doing it again for sanity purposes.
 

1. What are Christoffel symbols?

Christoffel symbols, also known as the Christoffel symbols of the second kind, are mathematical objects used in differential geometry and general relativity to describe the curvature of a manifold.

2. How are Christoffel symbols calculated?

The Christoffel symbols are calculated using the metric tensor and its derivatives. The specific formula for calculating them varies depending on the coordinate system being used.

3. What is the significance of the Christoffel symbols?

The Christoffel symbols play a crucial role in understanding the curvature of a manifold and are used in various mathematical and physical applications, including general relativity, differential geometry, and mechanics.

4. Can Christoffel symbols be visualized?

While Christoffel symbols themselves cannot be visualized, they are used to calculate the components of the Riemann curvature tensor, which can be visualized as a measure of curvature on a manifold.

5. Are Christoffel symbols unique?

Yes, Christoffel symbols are unique for a given metric tensor and coordinate system. However, they can be transformed by a change of coordinates, similar to how vectors can be transformed under a change of basis.

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