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That surprises me. I know I’m not very far along, but I still had the same impression just from the way it’s discussed in Collier 6.7.

OK, nice work! I uploaded the PDF and added a link to it, to your original comment up above.

Actually I think only “admins” can upload stuff. This is an unfortunate shortcoming of the software we use. I think the restriction if for security, since the forum software is meant to be used for public forums.

I can make you an admin if you want, but…[Read more]

Sorry. I missed that. I see it now. I’ll post it up above, in a minute.

I could not figure out how to post or send an attachment here, so I attached my area calculations to my email response.

UPDATE:

OK, maybe I should have been able to figure this out from what Stefan said above, but I got if from these videos:
Relativity 107c: Starting around 19 minutes.
Tensor Calculus 24: Starting around 18 min, and especially around 22min.

So, I think what’s happening is that, in Schwarzschild space, the stretching and squeezing cancel each…[Read more]

@stefan, I read through that. Nice site by the way! But I’m still confused. At one point it says: “The physical meaning of the Ricci tensor is that it describes how much the spacetime volume of an object changes due to gravitational tides in general relativity.” And it gives a really nice explanation (with pictures!)

But then later on, it does…[Read more]

I have been reading about the interpretation of the Ricci tensor and scalers. I found information on a website called Profound Physics (https://profoundphysics.com). They have good articles on a variety of physics topic, including special and general relativity. Link to the article on the Ricci tensor:…[Read more]

For whatever it’s worth, here’s what I got for the non-zero entries of the Riemann Tensor
Riemann-Nonzero.pdf

I wanted to post a warning that something I’ve said recently was totally wrong. I mentioned (more than once) that I believed the Ricci Scalar represented the “intensity of curvature” of the space. Not true.

I ran my code on the Schwarzschild metric and much to my surprise both the Ricci Tensor and Scalar were zero. At first I thought there was a…[Read more]

Thanks; I remember quickly skimming that now.

I don’t know everywhere he talks about it, but I think the idea is first introduced on page 144.

@mike @scott @stefan

Does Collier talk about the process of lowering an index other than on page 160?

It’s a fun challenge when I have an occasion to write a smallish program. Plus I could stand to gain more familiarity with JavaScript and DOM.

I put the source on GitHub: https://github.com/quadboston/Collier-problem-6.9

D’oh!
Yes, you’re right.

I’m really excited that someone else is writing code to do these things!

We’re talking about your 14 and 15, right? I believe those are zero, because they’re the derivative of a function of theta with respect to phi. Right?

Mike, I think our results are compatible except for R-upperɸ-lowerɸθɸ and R-upperɸ-lowerɸɸθ.

I wrote a JavaScript program to do the tedious part of the Riemann curvature tensors and display the results step-by-step up to a certain point, so that I can enjoy(?) doing the rest manually. I haven’t simplified it yet so I don’t know if I’ll get the same results as Mike. I’ll do that in the coming…[Read more]

I think I’ve got my python code that calculates all the tensors working. Though it would still be good to see if anyone else gets the same results. I’m doing all the tensors the way Collier does with the exception of the Ricci tensor and scalar. For those I start by contracting the first and third indices of Riemann, where Collier contracts the…[Read more]