Problem in xCoba tensor component computation of contracted indicies

[Gurmeet Singh]

Hello everyone,

I am new to this xCoba computation so I want to calculate the component of the equation of motion in general relativity with R^2 correction.  Everything goes well until I added the RicciScalar^2 term in Einstein Hilbert action after that calculation becomes complex and it doesn't calculate the components. 

If anyone has some idea to resolve the issue, please give some input. I attached the file.

[Jose]

Hi,

I've modified your notebook to do this computation using CTensor, which is much easier.

Cheers,

Jose.

[Gurmeet Singh]

Hi Jose, 

Thanks for the response. 

One more thing I want to ask, can I extend this calculation with terms like Ricci^2 or Riemann^2 or Gauss-Bonnet term.

if yes, where do I suppose to change in /rule command?

[Jose]

Yes, you can extend this computation to include other curvature tensors. You just need to add more replacement rules changing the abstract tensor (say RiemannCD[-a, -b, -c, d]) by the corresponding explicit tensor (say CTensor[array of components, bases][-a, -b, -c, d]). The Ricci and RicciScalar rules are already present in the notebook I sent, but not the Riemann and Einstein rules.

Jose.