ecterrab

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15 years, 286 days

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These are replies submitted by ecterrab

@mthkvv 

I returned to this today, and have a few comments. I fail to see the problem formulated as in the book. Instead of 96.5 you start from some other expression,

where, in addition, you missed the red dot (multiplication) you see inserted in this image above. The way you entered, %g_[determinant])(...) was a function, not a product, and that generated that error message about the indices (so not an index issue, the error message is correct, but an input issue in your worksheet).

In my previous reply, I suggested a step-by-step based on entering 96.5, that is 

So, define your t[i,k], your h[i,k,l] as in the book, then isolate t[i,k] etc. I am not sure the steps I outlined in the previous reply will take you to 96.8, I didn't try, but if you formulate this correctly I can help you in doing that derivation in the computer.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

Did you read all of my answer? Because the first problem you mention is the one I mentioned, and that I also mentioned it "to appear resolved in the next Updates." So what is your point?

About breqn, I respectfully disagree. I find it nowadays an excellent package. By the way, a) the use of breqn passed almost 3 months of intensive testing in the beta forum, and passed that test with flying colours. As an example of that, see this Mapleprimes post.  b) In general: it is not good practice to say that something done by other people doesn't work, in a sort-of-full-disqualify, and without providing one example of what are you referring to. The a) is for your information; regarding b), serious, there are no good reasons for that, although this is just my opinion, and again it is all ok if you feel different about it.

Best

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Sradharam 

The way to go with computer algebra systems is to type a couple of words in their help system. Try that. Type Lie algebras in Maple's help. You will see two packages popping up, not one. DifferentialGeometry, the other package, is the state-of-the-art. That said, your statement of the problem is also unclear. What do you mean, exactly, by "Lie subalgebra for finding optimal solutions"? You can help people help you by clicking that green arrow and uploading a worksheet with your problem formulated, up to what you know how to do it, and then text with your question.

So please check the help system, and if what you need is not found in the help pages (or you are lost in the amount of them), please post a worksheet with your problem; people here will try to help you.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

 

@subzero 

Also, in 3-D the Weyl tensor has all its components = 0. BTW, in the input that results in (12), it should be Ricci, not Ricch.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@subzero 

Setup(dimension = 3). Check the help page of Physics:-Setup

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@subzero 

Download Gamma_R_Ri_W.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@subzero 

Your question is too specific to answer without seeing details. First of all, do you have Maple? If so, open please the help page ?Physics:-Christoffel. There is a defining formula there. The starting point is for you to tell, in formulas, on a Maple worksheet, exactly what (apparently different?) definition you want to use. Without that I can't help you more than the generic comments in the previous two replies, or saying my opinion, that Maple has more thorough and flexible tools for working with general relativity than any other platform (as in: for GR, if not in Maple, then nowhere).

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

UPDATE Mar/21: This is now fixed and the fix distributed for everybody using Maple 2021 within the Maplesoft Physics Updates v.934 and newer.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

UPDATE Mar/21: This is now fixed and the fix distributed for everybody using Maple 2021 within the Maplesoft Physics Updates v.934 and newer.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@subzero 

You can't do it the way you say, the same way you can note redefine the exponential function and expect that everything else uses your new definition. Christoffel has a unique definition. That definition is used in several places. If you post your problem or an example that illustrates what you need more specifically, then one could imagine a solution.

Meantime, what you can do is ignore entirely that all these tensors exist predefined according to textbook definitions (Christoffel, Ricci and Riemann) and define yours, say C, R, Ri, where your C I imagine is in terms of the metric g and its derivatives, R is some contraction of Ri and Ri is a function of C, g and its derivatives. To define a W traceless tensor related to Ri is also trivial. All that can be done defining tensors as explained in the Physics,Tensors help page, the sections on how to define tensors. Actually, it wouldn't take more than 5 minutes to define three or four tensors like those.

To summarize, you can always ignore the existing definition of these tensors and work with an entire set of other ones that you define with ease in a few minutes at most. It is simpler if you could show, on a Maple worksheet, more specifically, what you need and how do you intend to use it. There may be other more convenient solutions.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@nm 

Copy As LaTeX works pretty-well, and is a very nice feature of Maple 2021. Don't give up that. Why don't you write an email to support@maplesoft.com telling the problem? I'm sure they will do their best to help you diagnose and fix the problem, which, by the way, is not related to Physics, the Updates or anything else. I would try to uninstall Maple and then use a File Manager to wipe out every remaining for-sure. Then re-install; though I suppose you already tried that, anyway, support is the way to go, I think.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@nm 

It is difficult to imagine the problem; guessing here, could it be that you have another library interfering? Maybe some Maple 2020 library around in a personal directory ... or the Physics Updates installed by hand?

Take a look at the directories mentioned in the variable libname and make sure you don't have any additional libraries around. Then, Copy As LaTeX should work right away, even if you don't have the Maplesoft Physics Updates installed. And if you have it, as said below, I implemented a new option so that things get copied as output, not as input.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@mthkvv 

I looked; good feedback yours. Some improvements are needed here. I am busy at this moment. I will try to address them the next week, partially or entirely, and write here again.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@mthkvv 
Yes. I think you can get (96.8) directly from the definition of t you do with the so small-expression (96.5). So isolate t[~i, ~k] in (96.5), then convert(%, Christoffel). You may need to collect g_, factor, or the like to get it written so organized, but you are expected to get (96.8). Take a look at the Sec II, subsection 20 of ?Physics,Tensors to familiarize yourself with the idea; the conversion network is vast and extremely useful for derivations like the ones you are pointing at in Landau's book.

Caveats: in the above, I'm saying, but didn't actually do the computation - if you do the computation and find something not working as I am saying, please let me know; in that case, I will take a closer look.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@mthkvv 

Yes, you can. Define the tensors, lambda and h (92.[2,3]), then T is the EnergyMomentum (or use the Einstein's tensor); next, define `t` using (96.5), then input (96.8) and verify equality, for instance as done in the previous reply above. Once you verified you entered your tensor definitions without typographical mistakes, go with convert((96.8), g_), and you will receive (96.9).

Important: all these things are explained in ?Physics,Tensors, including the conversion network in Sec II, subsection 20; then you already know how to define the tensors (from your kerr.mw). Using inert tensors sometimes help with these demonstrations (there is always more than one way to do them), and any intermediate tensorial manipulation is also expected to be explained in ?Physics,Tensors. If it is not there, let me know, please, and I will include it.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

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