# plotting – Equipotential surfaces using parametric plot So I’m trying to plot lines on which the following function is a constant
$$frac{left(-Sigma (r,0.99,theta )+2 r^2-0.99^2 r sin ^2(theta )right)^2}{Delta (r,1,0.99) Sigma (r,0.99,theta )^3}+frac{0.99^4 sin ^2(theta ) cos ^2(theta ) Delta (r,1,0.99)}{Sigma (r,0.99,theta )^4}$$
where $$Delta (r,M,a):=a^2-2 M r+r^2quadtext{and}quadSigma (r,a,theta):=a^2 cos ^2(theta )+r^2.$$
I’m using the following code which was motivated from the second comment on this post

``````(CapitalSigma)(r_, a_, (Theta)_) := r^2 + a^2*Cos((Theta))^2;
(CapitalDelta)(r_, M_, a_) := r^2 - 2 M r + a^2;
cValues = {0.01, 0.1, 0.08, 0.06, 0.003, 0.005, 0.12, 0.14, 0.2, 0.15, 0.02, 0.04, 0.03, 0.18, 0.22, 1.5, 2.3, 0.002, 0.0025, 0.003, 0.0015, 0.0018, 0.0023, 0.0011, 0.0009, 0.0008, 0.0007, 0.0006, 0.0005};
trajectories = Function({x, y, r, (Theta)},  (CapitalSigma)(r, 0.99, (Theta))^(-3)*(CapitalDelta)(r, 1, 0.99)^(-1)*(2 r^2 - (CapitalSigma)(r, 0.99, (Theta)) - 0.99^2 r Sin((Theta))^2)^2 + (CapitalDelta)(r, 1, 0.99)*0.99^4*(CapitalSigma)(r, 0.99, (Theta))^(-4) Sin((Theta))^2 Cos((Theta))^2);
ParametricPlot({Sqrt(r^2 + 0.99^2)*Sin((Theta)), r Cos((Theta))}, {r, 0, 5}, {(Theta), 0, Pi/2}, PlotStyle -> {Green}, MeshFunctions -> {trajectories}, Mesh -> {cValues})
``````

and it gives the output as shown here (the second one is the zoomed out version of the first).  As you can see, the bottom left corner has strange behavior and I’m not sure why. I also do not understand what the `trajectories` part of this code is doing, more precisely why does the `Function` have 4 arguments in the beginning? Please help.

(context: I’m trying to plot the lines of constant acceleration in Kerr spacetime) Posted on