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I use the following code to generate a plot:

a[r_] := A  r^3/( r^3 + A^3 L1^2);
Rg[r_] := (2 ma r^3)/( r^3 + 2 ma^3 L^2);
\[Rho][r_] := r^2 + a[r]^2*Cos[\[Theta]]^2;
\[CapitalDelta][r_] := r^2 - Rg[r] r + a[r]^2;

g = {{-(1 - (Rg[r] r)/\[Rho][r])(*G[r]*), 0, 
    0, -((a[r] Sin[\[Theta]]^2 r Rg[r])/\[Rho][r])}, {0, \[Rho][
     r]/\[CapitalDelta][r], 0, 0}, {0, 0, \[Rho][r], 
    0}, {-((a[r] Sin[\[Theta]]^2 r Rg[r])/\[Rho][r]), 0, 0, 
    Sin[\[Theta]]^2 (r^2 + a[r]^2 + (
       a[r]^2 Rg[r] r Sin[\[Theta]]^2)/\[Rho][r])}};

v1 = {Sqrt[-(g[[1, 1]] - g[[1, 4]]^2/g[[4, 4]])], 0, 0, 0} ;

(v1.g.v1) /. {A -> 6, ma -> 10, L1 -> 0.1, L -> 0.1};

Plot3D[%,{r,0,20},{\[Theta],0,Pi}]

and I get the plot:

enter image description here

Now I want to add a vertical plane at r=18. How can I do that?

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  • 1
    $\begingroup$ Show[plot, Graphics3D @ InfinitePlane[...]] $\endgroup$ – Kuba Dec 13 '19 at 10:25
  • $\begingroup$ @Kuba Could you please be more explicit? In the documentation I have found that I should substitute three coordinate points in [...], but I don't get which. I have tried variuos combination, but I always get the same plot that I have reported. $\endgroup$ – mattiav27 Dec 13 '19 at 10:31
  • $\begingroup$ Have a look at Hyperplane. $\endgroup$ – b.gates.you.know.what Dec 13 '19 at 10:36
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More information about plane is needed (Thanks to @Kuba's comment)!

Show[{Plot3D[%, {r, 0, 20}, {\[Theta], 0, Pi}, AxesLabel -> Automatic]
, Graphics3D[InfinitePlane[{18, 0, 0}, {{0, 1, 0}, {0, 0, 1}}]]}]

enter image description here

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