Im trying to use both packages together in order to study the Bondi-Sachs metric. I'm having some trouble making it work.
- I have my main manifold $M$, and a "sub-manifold" $S$ which is the surfaces of constant $t$ and $r$. Some tensors are defined on $S$ which has a metric $S_{ab}$ and these are used to define tensors on $M$. I tried defining a manifold M and a vector bundle S but its not working:
DefManifold[\[ScriptCapitalM], 4, {a, b, c, l}]
DefBasis[red, Tangent\[ScriptCapitalM], {0, 1, 2, 3}]
DefChart[bondi, \[ScriptCapitalM], {0, 1, 2, 3}, {u[],
r[], \[Theta][], \[Phi][]}, ChartColor -> Blue,
FormatBasis -> {"Partials", "Differentials"}];
DefVBundle[esf, \[ScriptCapitalM], 2, {A, B}]
- I want to define abstract tensors xTensor style and then define the metric in terms of these Tensors and coordinate functiones. For example the angular part of the metric is
$$g_{ab}=S_{ab}+\frac{1}{r} C_{ab}+\frac{1}{r^2}d_{ab}$$ in which im mixing the coordinate r and some abstact tensor. I want to be able to compute stuff like the Riemann tensor from this metric.
I'm new to these packages so excause me.
