a problem with CTensor

[Mohammad Hassan Vahidinia]

Dear all,

I've tried to check the Riemann tensor of an AdS space via the maximally symmetric form of the Riemann. But, it seems that the CTensor has a problem to recognize indices ordering and so the calculation leads to a wrong result.

Best, 

Mohammad

[Pedram Karimi]

Dear Mohammad Hassan

I think the problem is related to different ways of rendering the matrix by Mathematica and inner structure of xAct. You can define the constant curvature Riemann tensor without "Head" command then you will see all the results of xAct is what you are expecting. You can find the new notebook by attachment.

I hope someone would clarify what goes wrong with the way you write Riemann tensor.

Best,

Pedram

[Jose]

Hi,

Yes, Pedram is correct. Head should not be used to extract the CTensor[...] object without first checking/imposing a definite order of indices. The xCoba command ToCCanonical will sort indices in CTensor[...][indices] as ToCanonical would do it in tensor[indices], so a possible solution is to replace

riem = Head[...]

by

riem = Head[ToCCanonical[...]]

and then the rest of the computation will work as expected.

In general, it is better to work with indices, because then any index order will be fine, and equations look clearer. In your case, replace the definition of riem above by

riem[a_, b_, c_, d_] := \[ScriptG][a, d] \[ScriptG][b, c] - \[ScriptG][a, c] \[ScriptG][b, d]

and then the rest of the computation will work as expected too.

Finally, check the consistency between the specified metric signature list and the signs of the metric components. xCoba will not always catch that type of problem, and results might be wrong.

Cheers,

Jose.

[Mohammad Hassan Vahidinia]

Dear Pedram and Jose,

Thank you so much for the clarification. I should learn more about the inner structure of the xAct.

Best,

Mohammad