Polar plot for the event horizon of a Kerr BH

In summary, the conversation discusses creating a graph of the event horizon of a Kerr black hole using a simple command of polar plot. However, there is an issue with the point where the event horizon and static limit meet, as it should be on the y-axis but is instead on the x-axis. The person has tried various solutions but has not been able to fix the problem. They also mention not wanting the graph to be in 3D. Finally, it is suggested to use the sine instead of the cosine to resolve the issue.
  • #1
Sumarna
7
0
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]
 
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  • #2
Just use the Sine instead of the Cosine:

bl.vs.ks.png
 

Related to Polar plot for the event horizon of a Kerr BH

1. What is a polar plot for the event horizon of a Kerr BH?

A polar plot for the event horizon of a Kerr BH is a graph that illustrates the shape and orientation of the event horizon of a rotating black hole, known as a Kerr black hole. It plots the distance from the black hole's center (radius) on the horizontal axis and the angle (polar angle) on the vertical axis. This type of plot is used in general relativity to analyze the properties of rotating black holes.

2. How is the polar plot calculated for a Kerr BH?

The polar plot for a Kerr BH is calculated using the Kerr metric, which is a mathematical expression that describes the properties of a rotating black hole. This metric takes into account the black hole's mass, spin, and charge to determine the shape and orientation of the event horizon. The calculations involve complex mathematical equations and are typically done using computer simulations.

3. What information can be obtained from a polar plot for a Kerr BH?

A polar plot for a Kerr BH can provide information about the shape, size, and orientation of the event horizon of a rotating black hole. It can also reveal the rotation rate of the black hole and the spin direction. This type of plot is essential in studying the effects of gravity and space-time around a Kerr black hole.

4. How does a polar plot for a Kerr BH differ from a regular polar plot?

A regular polar plot typically plots points in a two-dimensional plane, whereas a polar plot for a Kerr BH plots points in a three-dimensional space. This is because the event horizon of a rotating black hole exists in three dimensions, and the polar plot is used to visualize its shape and orientation. Additionally, a regular polar plot may use different units on the axes, while a polar plot for a Kerr BH typically uses units of distance and angle.

5. What are the applications of a polar plot for a Kerr BH?

A polar plot for a Kerr BH is mainly used in astrophysics and general relativity to study the properties of rotating black holes. It can help us understand the effects of gravity and space-time around these objects and how they interact with matter and other celestial bodies. It also has practical applications in fields such as gravitational wave detection and space navigation.

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