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Christoffel Symbol blues

by genericusrnme
Tags: blues, christoffel, symbol
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genericusrnme
#1
Dec15-11, 05:58 PM
P: 615
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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quasar987
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Dec15-11, 06:56 PM
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Some math program like mapple?
graupner1000
#3
Jan4-12, 05:43 AM
P: 13
Quote Quote by genericusrnme View Post
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.

graupner1000
#4
Jan4-12, 07:47 AM
P: 13
Christoffel Symbol blues

Then again, I just came across this

http://www2.astro.psu.edu/~cduston/metriclist.pdf
genericusrnme
#5
Jan5-12, 07:22 AM
P: 615
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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