Hi everyone! I'm very new to xAct (and Mathematica in general) and I've been trying to learn how to properly use the tools of xCoba primarily.
I'm curently trying to calculate the components of the Riemann tensor in the linearized regime of gravity. To do so, i defined the background metric to be the flat metric in cartesian coordinates and also defined a perturbation tensor H with the Newtonian potential on the diagonal. Then, I calculated the Christoffel symbols in linear order of H, so far so good. Finally, I calculated the Riemman tensor using the Chistoffels calculated previously. The resulting tensor comes with indices [d, -a, -c,-b] when the result I expected was [-a, -b, -c, d]. I am having trouble to understand this behaviour and how to correct to get the desired result.
Attached to this message is a sample notebook displaying the problem and an image with the expressions used to calculate both the Christoffels and the Riemann tensor in the linearized regime (to first order in H).
Sorry if I'm missing something obvious here, I tried looking into some documentations but so far I havent been able to understand the main issue.
Thanks in advance for any help with this.
Kind regards.