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Joule Thomson expansion of black hole

I am trying to recreate the T-P plane of figure 3 in the article black hole J-T in Mathematica. I am following the procedure but cannot obtain the graph. I don't know exactly where am i doing wrong. Can any one tell me how to fix it? My notebook is attached here.

One does not need to read full paper...the relations in my notebook are sufficient. Logic is simple. Solving f(r)=0 gives a value of r. We name it 'rh'. Put this rh in 'temp' and plot the expression vs P. This should results like fig 3 in the article.

POSTED BY: Debojyoti Mondal
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Debojyoti also asked about this on Physics Forums, so I posted an answer there based on the content of his notebook, rather than reading his reference in detail: https://www.physicsforums.com/threads/black-hole-joule-thomson-expansion-in-mathematica.1064855
POSTED BY: Ronald Riegert

Well, we need largest positive root for r from f(r)=0 for any choice of parameters. Now q and M are fixed. But P is there. So we dont know what is largest postive root. I don't know how can we do that. Now even if i dont get a solution, it is sufficient to get an approximate expression of r in terms of P from f(r)=0. Is there any way to do that?
POSTED BY: Debojyoti Mondal
Eric Rimbey
Eric Rimbey
Posted 5 months ago

I was afraid you were going to say that. Look, you did exactly what you describe and it didn't work. It didn't work because you didn't choose a solution for rh. How am I supposed to know which solution to use? So, I guess I need to read the paper. But you tell me I don't need to read the paper. And around we go. You either need to provide more explanation, or choose a solution, or point me to the relevant parts of the paper, or wait for me to read the paper myself.
POSTED BY: Eric Rimbey

don't need to read full paper...the relations in my notebook are sufficient. Logic is simple. Solving f(r)=0 gives a value of r. We name it 'rh'. Put this rh in 'temp' and plot the expression vs P. This should results like fig 3 in the article. It may not be possible to solve exactly for r. There might be some different way. May be some way to combine the expressions for temp and the equation f(r)=0 in a single plot, i don't know.

POSTED BY: Debojyoti Mondal
Eric Rimbey
Eric Rimbey
Posted 5 months ago

I'd rather not read that whole paper to understand your question. Looking at the picture, though, it seems that we have some relation for T and P that is parameterized by variables q and M. If you just give us that relation, we can probably figure it out. It doesn't seem like your f is that relation--I don't see T in there and I don't know what r is.
POSTED BY: Eric Rimbey
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