GR Resource?

[darkmatter4brains]

Does anybody know a good place where you can look up Christoffel Connection coefficients and Riemann Tensor components for common metrics?

Thanks.

 

[ramparts]

Oh man up and calculate them yourself :lol: Seriously, though, the Christoffel symbols can actually be calculated pretty quickly using a Lagrangian method, though the Riemann tensor is still a pain... Otherwise, do you have Mathematica? There's a ton of free and not-so-free GR packages which will calculate all this quickly and painlessly. Let me know if you want either the method for calculating the Christoffel symbols or some Mathematica packages.

 

[darkmatter4brains]

Even the Lagrange method isn't that quick and easy - it just is, relatively speaking, compared to the chug and plug method via the metric. And like you said, it does nothing for the Riemann Tensor.

No, on Mathematica. But I might break down and buy it. But, I was hoping to find a free way to do this first

EDIT: btw, do you recommend a specific package for Mathematica?

Thanks!

 

[ramparts]

RGTC is free and does the job pretty well:

http://www.inp.demokritos.gr/~sbonano/RGTC/

But you can use Google and check out different ones.

But if you're posting on the forum, waiting for responses, and agonizing over whether to buy Mathematica, chances are you'd have saved time just calculating by hand. Plus it's better for your soul Do you really need to do this for a huge variety of metrics? May I ask what you need this for, by the way?

And the Lagrange method totally is quick and easy! Just solve the Lagrange equations four times (which you know isn't hard or tedious) and you can read all the non-zero components right off.

 

[darkmatter4brains]

thanks for the link and info

My reason - I'm surprised you ask. Mainly, after calculting these by hand many times, it gets old after a while. Don't you agree?

Quick and Easy, huh? I propose a challenge then .... calculate the connection coefficients for the Rotating Black Hole (Kerr) Metric utilizing the variational approach. If you can do it in under 2 mins, I'll agree. That would probably fit my defiition of quick and easy. Oh, and when your two minutes is up ... you must have enough confidence that your connection coefficients are 100% correct, so you know you're not wasting the next hour of your life calculating Rieman tensor components utilizing incorrect christoffel connection coefficients - because only of them has to be wrong!

Oh, and then do that 200 more times ... and see if still seems as quick and easy

 

[ramparts]

I'm enjoying the Spanish sun, need to get to a guitar lesson in 20 minutes, and I am not calculating connection coefficients for the Kerr metric right now :lol: And I haven't done those calculations in a couple of years (I'm sure I will this fall!), but I think while 2 minutes is over-optimistic, 5 would be more than realistic. Maybe I'll try it later, if I get bored
But if you're doing it 200 times, then just buy Mathematica (or probably Matlab).

And I was more wondering what you were using it for - are you in research? I was under the impression you weren't in academia but I could be off-base.

 

[darkmatter4brains]

I'd even be impressed by 5 minutes, but then again I'm slow :lol: I have to be - I am prone to make mistakes. Not big ones, mind you ... but I am famous for losing minus signs and factors of two ... or gaining factors of 2 out of the blue, which is really weird!

No, I haven't been in academia for a while ... but, being a nerd, I do a lot of self study with physics still. I am also involved in a small group at work that this is for, but no real serious research you would find interesting.

I think you solved my problem and for free!! I have an OLD student copy of MATLAB at home, but that was too old to use a tensor package I found online. However, I totally forgot I have a newer version at work, yet old enough that I don't use it there. Problem solved! :lol:

 

[ramparts]

You're welcome