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

In summary, there are various ways to calculate the Christoffel symbols, but they can all be time-consuming.
  • #1
genericusrnme
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2
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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  • #2
Some math program like mapple?
 
  • #3
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.
 
  • #4
Then again, I just came across this

http://www2.astro.psu.edu/~cduston/metriclist.pdf
 
  • #5
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
 

What is a Christoffel Symbol?

A Christoffel symbol is a mathematical object used in differential geometry to describe the curvature of a space. It is a set of numbers that represent the connection between tangent vectors at a point in a space.

How are Christoffel Symbols calculated?

Christoffel symbols are calculated using the metric tensor of a space. The metric tensor is a mathematical object that describes the distance between points in a space. Using the metric tensor, the Christoffel symbols can be calculated using a specific formula.

What is the significance of Christoffel Symbols?

Christoffel symbols are important in the study of differential geometry and general relativity. They allow us to understand the curvature and geometry of a space, which is crucial in understanding the behavior of matter and light in the universe.

What is the relationship between Christoffel Symbols and the Levi-Civita connection?

The Levi-Civita connection is a special type of connection used in differential geometry. The Christoffel symbols are the coefficients of this connection, and they are used to define the connection and calculate its properties.

Are Christoffel Symbols unique for a given space?

Yes, Christoffel symbols are unique for a given space. They are determined by the metric tensor and the geometry of the space, so different spaces will have different Christoffel symbols. However, the same space can have different sets of Christoffel symbols depending on the choice of coordinates used to describe it.

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