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

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SUMMARY

This discussion focuses on the search for a comprehensive list of Christoffel Symbols for various metrics, including well-known examples like the Schwarzschild and Robertson-Walker metrics. Users recommend utilizing the Maple software along with the GRTensor package for efficient computation of these symbols, as manual calculation can be tedious and error-prone. The conversation highlights the complexity of obtaining a standardized list due to variations in coordinate systems and notation, which can lead to confusion.

PREREQUISITES
  • Understanding of general relativity concepts, particularly metrics.
  • Familiarity with Christoffel Symbols and their significance in differential geometry.
  • Basic knowledge of the Maple software environment.
  • Experience with the GRTensor package for tensor calculations.
NEXT STEPS
  • Explore the capabilities of the GRTensor package in Maple for tensor computations.
  • Learn how to compute Christoffel Symbols manually for various metrics.
  • Investigate the differences in notation and coordinate systems used in general relativity.
  • Research additional resources or databases that compile Christoffel Symbols for different metrics.
USEFUL FOR

Students and researchers in theoretical physics, mathematicians specializing in differential geometry, and anyone involved in general relativity who requires efficient computation of Christoffel Symbols.

Chaosmarch
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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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Maple + GRTensor package.
 
Thanks, that's a very useful resource, though I was looking for a list, analogous to a Table of Integrals.
 
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.
 

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