Where can I find a list of Christoffel symbols for calculation?

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    Christoffel Symbol
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Discussion Overview

The discussion revolves around the search for resources that provide a list of Christoffel symbols, akin to a table of integrals. Participants express the challenges of calculating these symbols by hand, particularly in the context of general relativity and various metrics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant inquires about books or websites that compile Christoffel symbols, highlighting the difficulty of manual calculations.
  • Another suggests using mathematical software like Maple for assistance.
  • A participant notes the potential confusion due to varying conventions and notations, suggesting that a list might not be universally useful.
  • There is mention of specific metrics, such as the Schwarzschild and FLRW metrics, which might have resources listing non-zero Christoffel symbols.
  • A link to a PDF resource containing metric lists is provided by one participant.
  • Another participant discusses the efficiency of calculating connection 2-forms using differential forms, seeking further information or book recommendations on the topic.
  • One participant mentions having created a Mathematica notebook that can compute Christoffel symbols for arbitrary coordinates and offers to share it.

Areas of Agreement / Disagreement

Participants generally agree on the difficulty of calculating Christoffel symbols by hand and the potential utility of software tools. However, there is no consensus on the availability or usefulness of a comprehensive list of symbols due to varying conventions.

Contextual Notes

Limitations include the lack of specific references to books or resources that list Christoffel symbols, as well as the dependence on the context of different metrics and conventions.

Who May Find This Useful

This discussion may be useful for students and professionals in physics and mathematics who are dealing with general relativity, differential geometry, or tensor calculus, particularly those seeking computational tools or resources for Christoffel symbols.

genericusrnme
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Is there any book out there or website or something that has a list of christoffel symbols, something analogous to a table of integrals
The amount of times I've had to calculate christoffel symbols by hand is unreal and let me tell you, chugging through tensors on a moving bus is hard enough without all that extra work..

can anyone help?
 
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Some math program like mapple?
 
genericusrnme said:
Is there any book out there or website or something that has a list of christoffel symbols, something analogous to a table of integrals
The amount of times I've had to calculate christoffel symbols by hand is unreal and let me tell you, chugging through tensors on a moving bus is hard enough without all that extra work..

can anyone help?

I know what you mean, calculating the Christoffel symbols by hand can be an absolute nightmare. But given all the different conventions and notations, a list would be confusing to the point being useless for most people.

However, if you are trying to do it for it for a commonly used metrics like the Schwarzschild (which, I would like to add at this point, is pronounced like "shwarz-shild" and not "swarz-child") or FLRW metric, you might be able to find a book that lists all the non zero ones. I remember a cosmology book(though not which one) that did just that for the FLRW metric.

Alternatively, if you know about differential forms it is considerably quicker to calculate the connection 2-forms.
 
Then again, I just came across this

http://www2.astro.psu.edu/~cduston/metriclist.pdf
 
oh wow, I completely forgot that I posted this

Alternatively, if you know about differential forms it is considerably quicker to calculate the connection 2-forms.

I know about differential forms but not in connection with anything that'd help me find anything out..
Could you provide more information or the name of a book that'd help me?

Some math program like mapple?

I managed to get something to do the job in Mathematica for any arbitrary co-ordinates

If anyone is interested in the .nb I made that does this I'll upload it somewhere for you to use as you please
 

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