## 182 Reputation

4 years, 124 days

## So it is 2023, will upgrade to 2024 - th...

Thank you for this. I will upgrade to 2024 as soon as possible and hopefully all my issues will be resolved.

Regarding the physics, I have been rather opaque as this does not seem like the forum to properly discuss it. However I will say that I agree with everything you have said, I am simply just exploiting some previous knowledge and large amount of symmetry in my problem. Iff I solve the system simulattenously the consistent solution is the one which solves any of the first order ODEs that come from the field equations.

## Still not working for me...

In general yes you are correct but this spacetime a high degree of symmetry and a consistent solution for the unknown function can be found from solely solving the one component.

Set c_1 to zero in the last solution.

However, beyond this point I still do not get what you get.

So this makes me think there is something weird going on with my Physics package and yours is working fine?

## Physics omitted...

I omitted all of the physics which looking back might have been a bad idea.

So what I am interested in doing is solving for the metric function f(r) which is a solution to the modified graviational field equations which are R[a,b]=0. But then again the field equations could also be written as R[~a,b]=0 or even RR[~a,~b]=0. So the issue is it does not matter how you write the equations when you are trying to solve for the functions.

I am not suggesting that R[1,1]=R[~1,1]. I am saying that the solution for f(r) from the field equations should be the same regardless of how we solve - they are not. Secondly if we use the definition R[~1,1] = g_[~1,~a]R[a,1] You can see that this does not match what we get from the tensor I define. I did this in a modified sheet which no longer has the cross-term in the metric so we avoid the taylor series.

IndexQuestionMOD.mw

## Notation questions...

Can you clarify some of your notation. Is u an unkown function, does it depend on all the variables? What does u_x represent?

Do you want L to operate on T and vice versa or is it multiplication after it operators on some function?

If you can clarify this I think I can write something down relativietly quick, in the mean time you can always do something like this.

 > restart;
 > with(PDETools):declare(F(x))
 (1)
 > X:=x,y,z
 (2)
 > L:=u^2*%diff(F(X),x\$2)+%diff(F(X),y)
 (3)
 > eval(L,[F(X)=sin(x),%diff=diff])
 (4)

To create operators.

## Thanks to both...

Thank you both @acer @Rouben Rostamian for your replies.

I will repost.

## Because you still have unknowns...

In your second problem you have not specified n, S and Nc. If you do that from what you say in your "a" defintions it runs for me.

Always make sure there are no unkown variables in your boundary conditions otherwise it will not run.

See attached.

SCM2_response.mw

If you can upload your worksheet with your attempted solution, or provide more details to what you exactly are looking to solve this would be helpful.

## Issues with Physics...

You have some issues in your physics. The final solution in your image is not the solution of a spacetime with that stress energy distribution. That solution solves the vacuum field equations with a cosmological constant.

Please keep on eye on this thread as I will write an updated solution shortly.

## I always forget about that......

Thanks for reminding me of that option, I fail to remember that option exists when I do calculations with Lambda.

Can you give some more information about the stress-energy tensor? It is incomplete currently but I believe you are using a perfect fluid?

Lastly here is the method for solving just the 2+1 with a cosmological constant and no stress-energy. Once you give more information of confirm it is a perfect fluid I will update the response.

Response.mw

## The Green Arrow...

The green arrow that appears at the top of the text box (see image below)

Click on it, go to choose files as it says and click on your saved worksheet then click upload and insert link.

## Post Worksheet...

Or at the vary least post the ODEs you are working with.

You can use the green arrow to upload your worksheet or images.

## I just saw this.....

Hello, I am sorry for replying so late.

The desired output should be:

Details can be found in: https://physics.stackexchange.com/questions/93157/variation-of-modified-einstein-hilbert-action where some terms have been ignored.

Thank you for taking a look into this.

## ODEs?...

Just out of curiousity what are the exact ODEs you are trying to solve?

## Thanks!...

It does do rather interesting things in the negative region..something I had not thought about.

Is there any portion of the code that does deal with stepsize/speed? Not that I want to "speed up" the process just more of a curiousity on how it works.

The positive result is also interesting, not what I expected. I will keep tinkering with the parameter ranges and see if anything can occur. I appreciate this worksheet, it appears my attempt was far too simplistic.

Thanks!

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