xCoba - Differences between DefTensor and CTensor approach

[Alejo Hernandez]

Hi everybody,

I`ve recently started to learn how xCoba works and i have some difficulties in order to define some vectors in terms of it components and working with them.

My setup is as follows:

I'm trying to understand how the package works and I can't figure out how to define a new tensor from already defined tensors.

<< xAct`xCoba`

$Info = False; $CVVerbose = False; $DefInfoQ = False;

DefManifold[M, 4, IndexRange[a, q]]

DefMetric[-1, metric[-a, -b], CD, PrintAs -> "g"]

DefChart[B, M, {0, 1, 2, 3}, {t[], r[], x[], z[]}]

$Assumptions = {r[] > 0};

DefParameter[L]; DefScalarFunction[F];

metricarray = DiagonalMatrix@
  {-F[r[]], 1/F[r[]], r[]^2/L, r[]^2/L}

MetricCompute[metric, B, All, CVSimplify -> Simplify]

(* I`m trying to define a J tensor as an Einstein tensor plus a cosmological constant term *)

DefTensor[J[-a, -b], M]

J[-a, -b] := EinsteinCD[-a, -b] - 3/L metric[-a, -b]

(* is it correctly defined this way? When i try to do *)

ToValues@ComponentArray@ToBasis[B]@J[-a, -b] // MatrixForm

(* it shows all the tensor components as expected, but when i ask MMA to show a single component, it refuses and only prints J_00 *)

ToValues@J[{0, -B}, {0, -B}]

I don`t know what`s happening here. Please, could some one help me?

Also, i`d like to grasp what the difference would be in using the DefMetric/DefTensor approach vs the SetCMetric/CTensor one *)

Regards!