wormhole thin shell

This is faulty code in both C and Wolfram...

The main paper is:

Adria Delhom, Caio F. B. Macedo, Gonzalo J. Olmo, Luís C. B. Crispino (2019), Absorption by black hole remnants in metric-affine gravity. arXiv:1906.06411v1 [gr-qc] DOI 10.1103/PhysRevD.100.024016

This software was developed using GSL library, glib and Wolfram (using jupyter with the free Wolfram engine) I've done all the development in Windows so I've used the MSYS2 system. You can use Chocolatey or install MSYS2 directly.

After that you just have to install the GSL and glib packages using pacman. pacman is very convenient...

GUI

The GUI was made with Tcl/Tk You need one tcl distribution to use the GUI (but you don't need the GUI to use the program). Another useful tool is gnuplot, you can install it with pacman too.

Partial results

I was not able to extend the Gauss hypergeometrical function, 2_F_1, to calculate equations (4) and (8) using GSL (maybe Arb would be a better choice for this...) so I decided to use Wolfram. Compare the wolfram code to calculate the tortoise coordinates

(* Funciones *)
z[x_] = Sqrt[(x^2 + Sqrt[x^2 + 4]) / 2];
zp[x_] = 1 + 1 / z^4 /. z -> z[x];
zm[x_] = 1 - 1 / z^4 /. z -> z[x];
h[x_] = -1 / dc + Sqrt[z^4 - 1] (Hypergeometric2F1[1 / 2, 3 / 4, 3 / 2, 1 - z^4] + Hypergeometric2F1[1 / 2, 7 / 4, 3 / 2, 1 - z^4]) / 2 /. z -> z[x];
a[x_] = (1 - rSbyrc (1 + dc h[x]) / (z Sqrt[zm[x]])) / zp[z] /. z -> z[x];
zyy = a[x] zp[x] D[a[x] zp[x] D[z[x], x], x];
tortoiseXY = NDSolveValue[{x'[y] == a[x[y]] zp[x[y]], x[yL] == yL + 14.}, x, {y, yL, yR}];

with the equivalent in C an GSL tortoise There's no colour...

unfortunately I was not able to calculate the coeffcients R & T to calculate the partial absorption cross section... so I decided to use wolfram to calculate the 2_F_1 and use the results in the C code to get sigma_l. But I was not able to do it... and this's the cause

as you can see R + T != 1 so I cannot go ahead and calculate sigma_l.

I'm very confident that the correct results are almost in the wolfram code... but some work is need to get to the goal. In the C code the only flaw is the analytic extension of 2_F_1 as the code has good results in the Schwarzschild and Black Bounce cases.

Documentation

For more information you can consult the pdf

hykrion / wormhole-thin-shell Goto Github PK