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

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Discussion Overview

The discussion revolves around the search for a list of Christoffel Symbols for various metrics, including well-known examples like the Schwarzschild and Robertson-Walker metrics. Participants explore resources and tools that could assist in obtaining these symbols, as well as the challenges associated with their computation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about a list of Christoffel Symbols for various metrics, expressing a desire for a resource similar to a Table of Integrals.
  • Another participant suggests using the Maple software along with the GRTensor package as a potential solution.
  • A third participant provides a link to a website that may contain relevant information on the topic.
  • One participant cautions that a list of symbols could be confusing due to variations in coordinate systems and notation, even for the same physical metrics.
  • This participant also recommends using computer programs like Maple for calculating the symbols instead of manual computation, which they find tedious.
  • It is noted that computing the Christoffel symbols is often a homework problem, particularly for the Schwarzschild metric, and that doing it by hand is advisable only a few times for understanding.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility and utility of a comprehensive list of Christoffel Symbols, with some advocating for computational tools while others highlight the complexities involved in such a list.

Contextual Notes

There is an acknowledgment of the dependence on coordinate systems and notation when discussing Christoffel Symbols, which may lead to confusion in any proposed list.

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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