How can I find the unknown function? `V (r)`

specifying the metric `met`

in this gravitational theory? I have defined the variety as:

```
DefManifold[M, 4, {[Alpha], [Beta], [Sigma], [Delta], [Iota],
[Mu], [Omicron], [FinalSigma], [Tau], [Upsilon], [Chi],
[Omega], [Nu], [Rho], [Gamma]}]
```

and also a table like:

```
DefChart[[ScriptCapitalB], M, {0, 1, 2, 3}, {t[],
r[], [Theta][], [Phi][]}, ChartColor -> Blue].
```

The Lagrangian of gravitational theory is:

```
[ScriptCapitalL] =
1 / (2 [Kappa]) (-two [CapitalLambda]0 + RicciScalarCD[]) ([Eta] P) //
NoScalar;
```

where

```
P = 12 RiemannCD[-[-[-[-[Mu], [Rho], -[Nu], [Sigma]]RiemannCD[-[-[-[-[Rho],
[Gamma], -[Sigma], [Delta]]RiemannCD[-[-[-[-[Gamma], [Mu], -[Delta],
[Nu]]+ RiemannCD[[[[[Rho], [Sigma], -[Mu], -[Nu]]RiemannCD[
[Gamma], [Delta], -[Rho], -[Sigma]]RiemannCD[[[[[Mu], [Nu], -
[Gamma], -[Delta]]-
12 RiemannCD[-[-[-[-[Mu], -[Nu], -[Rho], -[Sigma]]RicciCD[[[[[Mu],
[Rho]]RicciCD[[[[[Nu], [Sigma]]+
8 ricciCD[[[[[Nu], -[Mu]]RicciCD[[[[[Rho], -[Nu]]RicciCD[[[[[Mu], -
[Rho]];
```

The scalar function that appears in the metric is `V (r)`

and one can define it as:

```
DefScalarFunction[V]
DefConstantSymbol[n];
met = MatrixForm[{{V[r[{{V[r[{{V[r[{{V[r[]], 0, 0, 4 n V[r[r[r[r[]]Cos[[[[[Theta][]]}, {0, 0, 0,
0}, {0, 0, (r[]^ 2 - n ^ 2), 0}, {4 n V[r[r[r[r[]]Cos[[[[[Theta][]], 0, 0,
4 n ^ 2 Cos[[[[[Theta][]]^ 2 V
The
r[]]+ (r[]^ 2 - n ^ 2) Sin[[[[[Theta][]]^ 2}}]
```

Now, the question is, how to replace the metric in the field equations and how to find the potential `V (r)`

?