xCoba Problem: Covariant derivatives of scalar field

[Purnendu Karmakar]

Dear friends,

I am interested in applying de Sitter metric explicitly to an equation of motion (EOM) by using xCoba. Many Christoffel symbols are not converted to its values. The EOM involves derivative of a scalar field. (ATTACHING the file) 

It seems that ToBasis is working properly and converting to the red indices. However multiple times ToValues is not functioning in one of my cases. Result saturates after using few times of ToValues. 

de Sitter metric is much simpler than the Schwarzschild metric or Kerr metric. I used the similar techniques applied in the given example file for KerrNewmanExamples and SphericalSymmetry. 

I would appreciate if somebody kindly helps me to solve this issue. 

Thanks and Regards, Purnendu

[ghadir jafari]

Dear Purnendu

There is nothing wrong with your code. Just when several contracting covariant derivatives  occur, Christoffel symbols in not their natural form appear.  In your case they are two first indices up. 

note that "MetricCompute" only compute and store tensors in their natural form. To compute and store components with other form of indices we need to use the command "ChangeComponents".

See your file which I added the command and successfully computed your expressions. 

Other solution is to use the command "ImplodedTensorValues" in xTras package. http://www.xact.es/xTras/documentation/ref/ImplodedTensorValues.html

Best

Ghadir

[Purnendu Karmakar]

Dear Ghadir,

I appreciate very much for your suggestion and solution to that issue.

- I am curious to find out the source of the affine connection containing two upper indices, which is unusual. :)  

- I am not sure in which stage I have to apply the "ImplodedTensorValues" in xTras. I tried 
ImplodedTensorValues[CD, LHS2, BdS]
ImplodedTensorValues[CD, ChristoffelCDPDBdS[\[Alpha], \[Mu], -\[Nu]], BdS]

None of those works. LHS2 is a vector quantity. Would you kindly provide some more suggestion in implementing it?

Thanks and Regards, Purnendu

[ghadir jafari]

Dear Purnendu

See your file for solution with "ImplodedTensorValues" in xTras.

I just changed the name of the scalar, because it seems to have problems with label indices.

Regards

Ghadir