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Plotting issue with multiple parameter

Debojyoti Mondal
Posted 20 days ago

Here Setting M=60,g=0.3,P=0.002418/0.09 I want to Plot X^2 + Y^2 = rs^2 for T ranges from 0 to 0.21. Is there any way to do that? It should look like some region bounded by two concentric circles.

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haywards - Copy.nb
POSTED BY: Debojyoti Mondal
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I know that X^2 + Y^2 = rs^2 cannot be plotted for negative rs^2. I am saying that if, i am doing some mistake or not. rs must be positive. Kindly look at the article https://arxiv.org/pdf/2301.06120.pdf. The used equations 16-21 and 24,25 to produce figure 5. rs is given by equation 18 with f(r0)=1. I want to recreate that as I am trying to do something similar with more parameter and complex system.

POSTED BY: Debojyoti Mondal

Your formula for rs is different from formula (18) of the paper. Please check it.
POSTED BY: Gianluca Gorni

they assumed f(r0)=1. This will give the same formula as mine.
POSTED BY: Debojyoti Mondal

You want to plot X^2 + Y^2 = rs^2 where rs^2 is negative. Good luck.
POSTED BY: Gianluca Gorni

It seems that f[rp] is negative for your values of T, and rs is complex:

M = 60; g = 0.3; P = 0.002418/0.09;Clear[T];
solR = Simplify[
  Solve[T == 
     1/6  r  (8  P + (3 M (-2 g^3 + r^3))/(\[Pi] (g^3 + r^3)^2)) &&
    0 <= T <= 0.21 && r > 0, r, Reals],
  0 < T < 0.21]
Plot[Evaluate[f[rp] /. solR],
 {T, 0, .22}]
POSTED BY: Gianluca Gorni

I too found similar cases. It was done in fig:5 in https://arxiv.org/pdf/2301.06120.pdf . Also I don't need plot of f[rp]. I need plot of X^2 + Y^2 = rs^2 with T in said ranges.
POSTED BY: Debojyoti Mondal
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