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.
oh wow, I completely forgot that I posted this 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? 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