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I have made graph of event horizon of Kerr black hole by giving simple command of polar plot. The problem is that the point where the event horizon and static limit meets should be along y-axis but instead its on x-axis. I have tried everything but not getting it right.
What mistake I am making? Am i giving wrong command? I do not want it in 3D.
M = 1;
a = .7;
p1 = PolarPlot[-M + Sqrt[M^2 - a^2 (Cos[\[Theta]])^2], {\[Theta], 0,
2 \[Pi]}];
p2 = PolarPlot[-M - Sqrt[M^2 - a^2 (Cos[\[Theta]])^2], {\[Theta], 0,
2 \[Pi]}];
p3 = PolarPlot[-M - Sqrt[M^2 - a^2], {\[Theta], 0, 2 \[Pi]}];
p4 = PolarPlot[-M + Sqrt[M^2 - a^2], {\[Theta], 0, 2 \[Pi]}];
Show[p1, p2, p3, p4]
What mistake I am making? Am i giving wrong command? I do not want it in 3D.
M = 1;
a = .7;
p1 = PolarPlot[-M + Sqrt[M^2 - a^2 (Cos[\[Theta]])^2], {\[Theta], 0,
2 \[Pi]}];
p2 = PolarPlot[-M - Sqrt[M^2 - a^2 (Cos[\[Theta]])^2], {\[Theta], 0,
2 \[Pi]}];
p3 = PolarPlot[-M - Sqrt[M^2 - a^2], {\[Theta], 0, 2 \[Pi]}];
p4 = PolarPlot[-M + Sqrt[M^2 - a^2], {\[Theta], 0, 2 \[Pi]}];
Show[p1, p2, p3, p4]