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

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SUMMARY

This discussion centers on the search for resources listing Christoffel symbols, particularly for commonly used metrics like the Schwarzschild and FLRW metrics. Participants highlight the difficulty of calculating these symbols manually and suggest that a comprehensive list may be found in specific cosmology books. Additionally, they mention using tools like Mathematica for automating these calculations and recommend exploring differential forms for a more efficient approach to finding connection 2-forms.

PREREQUISITES
  • Understanding of Christoffel symbols and their applications in differential geometry.
  • Familiarity with metrics such as Schwarzschild and FLRW.
  • Knowledge of differential forms and their relation to connection 2-forms.
  • Experience with mathematical software tools like Mathematica or Maple.
NEXT STEPS
  • Research the specific cosmology books that list non-zero Christoffel symbols for the Schwarzschild and FLRW metrics.
  • Learn how to use Mathematica for calculating Christoffel symbols and connection 2-forms.
  • Study differential forms in the context of general relativity to enhance understanding of connection 2-forms.
  • Explore online resources or databases that compile lists of Christoffel symbols for various metrics.
USEFUL FOR

Mathematicians, physicists, and students in fields related to general relativity, particularly those seeking efficient methods for calculating Christoffel symbols and understanding their applications in cosmology.

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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