Einstein tensor with mixed indices

[Mattia Villani]

I am trying to calculate the Einstein tensor of some metric with mixed indices, i.e.

Einstein[cd][a,-b]

for specific values of a and b using xTensor and xCoba. However using

Einstein[cd][{0,ch},{0,-ch}]                               (*)

for example, will cause a massive slow down over

met[{0,ch},a]Einstein[cd][-a,{0,-ch}]              (**)

where met is the metric. In 6d (*) takes about 4 hours, while (**) is almost immediate. It is even worse in higher dimensions (I had to stop the calculations in 8d after 8 hours). Why is it so? I calculate the Einstein tensor as follows

MetricCompute[met, ch, "Einstein"[-1, -1], CVSimplify -> Together]

[Karim Dad]

Dear Mattia,

Thank you for the warm welcome. Please accept my apologies for the delayed response.

Since I did not have your exact metric specifications, I used an arbitrary metric to calculate the Einstein tensor components as a baseline.

I have attached a fully parameterized Mathematica notebook. You can plug in your specific metric components to directly evaluate the Christoffel symbols, Ricci tensor, and Einstein tensor.

Please let me know if you need any further assistance. I would be glad to help further.

Best regards,
Karim Dad

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