Chart changing in xCoba from abstract xTensor object

[Daniel Gálvez García]

Hello everyone.

I am a Relativist doing his first steps in the xAct world. So, any advice regarding my use of xAct or basic Mathematica that helps me improve will be reaaaally welcomed.

In the attached notebook I am working with a familiar spacetime metric, FLRW, to understand how the package works. I am trying to learn the most optimal way to compute stuff with xCoba and xTensor. What I am trying to do here is the following:

As per my understanding, xAct is most efficient when working with abstract objects. Therefore, it is convenient to use abstract computations during the calculation and, at the end, use a basis to to your result.

In the NB I first defined a manifold with an abstract metric. Second, I defined a Cartesian chart and assigned a matrix to be the covariant representation of that metric in that specific chart. I also defined the Spherical chart.

Then, I defined the transformation rule from the Cartesian chart to the Spherical one via derivatives, and told xCoba that the JacobianMatrix is the rule it must follow in order to change basis.

My problem is that I cannot get xCoba to show me the actual components of the metric (or any other) tensor in the new chart, it just colors the indices. Is there a way to implement this idea to xCoba? What am I missing?

TL;DR I want to be able to work with abstract objects and then, via a transformation matrix between bases together with its explicit definition in one basis, get the specific components of any tensor automatically.

Thanks in advance for your help. Any advice highly appreciated!!