Drawing Sphere to represent a black hole

Question

Can anybody tell me how to draw up a sphere inside a sphere?

What I mean is something like this:

Also where it says the different horizons be able to insert a mathematical expression? Also not in these poor colours something that looks kind of professional.

Any help much appreciated.

Answer 1

This can be done quite easily with TikZ, although you will have to think about the order you put the commands. In nodes you can use math mode:

Code

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{arrows}
\begin{document}

\begin{tikzpicture}
    \fill (-4,-4)   rectangle (4,4);
    \begin{scope}
        \clip (0:2.47) arc (0:90:2.47) to[out=225,in=100,looseness=1.2] (-1.1,-1.1) to[out=-10,in=225,looseness=1.2] (0:2.47);
        \shade[ball color=blue!30!gray!60!black,shading angle=180] (0,0) circle (2.5);
    \end{scope}
    \shade[ball color=green!70!gray] (0,0) circle (2);
    \begin{scope}
        \clip (0:1.95) arc (0:90:1.95) to[out=225,in=100] (-0.7,-0.7) to[out=-10,in=225] (0:1.95);
        \shade[ball color=green!30!gray!60!black,,shading angle=180] (0,0) circle (2);
    \end{scope}
    \begin{scope}
        \clip (0:2.45) arc (0:90:2.45) to[out=225,in=100,looseness=1.2] (-1.1,-1.1) to[out=-10,in=225,looseness=1.2] (0:2.45) -- (3,0) -- (3,-3) -- (-3,-3) -- (-3,3) -- (3,3) -- (3,0);
        \shade[ball color=blue!70!gray] (0,0) circle (2.5);
    \end{scope}
    \draw[stealth-,red] (0,0) -- ++(70:3) node[right] {$r=\int\limits_{0}^{2\pi}\sin(x)\ dx$};
    \draw[stealth-,green!70!black] (-0.7,1) -- ++(135:2) node[above] {$r=\frac{8^2+4^2}{8^2+6^2}$};
    \draw[stealth-,blue!90] (225:2) -- ++(225:1) node[below] {$r=\left(\frac{e^{\pi}}{\pi^e}\right)^{\sin(\pi)}$};
\end{tikzpicture}

\end{document}

Output

---

Edit 1:

To make the spheres look less glossy, you can define your own radial shading, or modify the ball shading (thanks to Yori for this answer)

Code

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{arrows}

\makeatletter
\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{-10bp}{10bp}}%
{   color(0bp)=(tikz@ball!50!white);
    color(10bp)=(tikz@ball!75!white);
    color(15bp)=(tikz@ball);
    color(20bp)=(tikz@ball!75!black);
    color(30bp)=(tikz@ball!50!black)
}
\makeatother

\begin{document}

\begin{tikzpicture}
    \fill (-4,-4)   rectangle (4,4);
    \begin{scope}
        \clip (0:2.47) arc (0:90:2.47) to[out=225,in=100,looseness=1.2] (-1.1,-1.1) to[out=-10,in=225,looseness=1.2] (0:2.47);
        \shade[ball color=blue!30!gray!60!black,shading angle=180] (0,0) circle (2.5);
    \end{scope}
    \shade[ball color=green!70!gray] (0,0) circle (2);
    \begin{scope}
        \clip (0:1.95) arc (0:90:1.95) to[out=225,in=100] (-0.7,-0.7) to[out=-10,in=225] (0:1.95);
        \shade[ball color=green!30!gray!60!black,shading angle=180] (0,0) circle (2);
    \end{scope}
    \begin{scope}
        \clip (0:2.45) arc (0:90:2.45) to[out=225,in=100,looseness=1.2] (-1.1,-1.1) to[out=-10,in=225,looseness=1.2] (0:2.45) -- (3,0) -- (3,-3) -- (-3,-3) -- (-3,3) -- (3,3) -- (3,0);
        \shade[ball color=blue!70!gray,opacity=0.90] (0,0) circle (2.5);
    \end{scope}
    \draw[stealth-,red] (0,0) -- ++(70:3) node[right] {$r=\int\limits_{0}^{2\pi}\sin(x)\ dx$};
    \draw[stealth-,green!70!black] (-0.7,1) -- ++(135:2) node[above] {$r=\frac{8^2+4^2}{8^2+6^2}$};
    \draw[stealth-,blue!90] (225:2.2) -- ++(225:1) node[below] {$r=\left(\frac{e^{\pi}}{\pi^e}\right)^{\sin(\pi)}$};
\end{tikzpicture}

\end{document}

Output

Answer 2

Quite similar in spirit to Tim Bombadil's more complete answer, but using a slightly different approach so the order of drawing is easier to manage. It only currently works for the "opening" with 90 degree arcs along the relevant axes as they are approximated with Bézier curves.

\documentclass[border=0cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,backgrounds}

% Constant taken from
%
% @article{riskus_2006,
%   author={Aleksas Ri\v{s}kus},
%   title={Approximation of a cubic bezier curve by circular arcs and vice versa},
%   year={2006},
%   journal={Information Technology and Control},
%   volume={35},
%   number={4},
%   pages={371--378}
% }
%
\def\k{0.55191496}

\tikzset{
    sphere color/.store in=\spherecolor,
    sphere scale/.store in=\spherescale,
    sphere color=blue,
    sphere scale=1,
    sphere/.style={
        ultra thick,
        line join=round,
        draw=#1!75!black,
        ball color=#1,
    },
    sphere inside/.style={
        shading angle=180,
        sphere=#1!25!gray!75!black
    }
}

\newenvironment{sphere}[1][]
    {
        \begin{scope}[x=(0:1cm), y=(90:1cm), z=(260:0.25cm), #1]
            \path [sphere inside=\spherecolor, scale=\spherescale] 
            circle [radius=1];
    }
    {
        \path let \n1={cos 10}, \n2={sin 10} in [sphere=\spherecolor, scale=\spherescale, even odd rule, opacity=0.5]
        circle [radius=1] 
        % Rotate 10 degrees around the y and x axes
        [x={(\n1, \n2^2, \n2*\n1)},
         y={(0, \n1, \n2)}, 
         z={(-\n2, -\n1*\n2, \n1^2)}] (0,1,0) 
                .. controls ++( 0, 0,\k) and ++(0,\k, 0) .. (0, 0, 1)
                .. controls ++(\k, 0, 0) and ++(0, 0,\k) .. (1, 0, 0) 
                .. controls ++(0, \k, 0) and ++(\k,0, 0) .. (0, 1, 0);
        \end{scope}
    }

\begin{document}

\begin{tikzpicture}[background rectangle/.style={fill=black}, show background rectangle]

\begin{sphere}[sphere scale=5, sphere color=blue]
    \begin{sphere}[sphere scale=4, sphere color=green]
        \begin{sphere}[sphere scale=3, sphere color=red]
            \begin{sphere}[sphere scale=2, sphere color=orange]
                \begin{sphere}[sphere scale=1, sphere color=yellow]

                \end{sphere}
            \end{sphere}
        \end{sphere}
    \end{sphere}
\end{sphere}

\end{tikzpicture}

\end{document}

Answer 3

ePiX is a col­lec­tion of batch-ori­ented util­i­ties for GNU/Linux sys­tems, creates mathematically accurate figures, plots, and movies with output format(PSTricks, tikz, or eepic macros) or as vector (EPS or PDF) image files for use with LaTeX, Unfortunately not available on traditional TeXLive/MiKTeX distro but can be installed on Linux distro (Ubuntu) with sudo apt-get install epix.

This drawing can be done in ePiX, if you don't mind using an external image file. (The coordinate grids in the compiled PDF aren't as prominent as in the png file below.)

Output

Code

 /* -*-ePiX-*- */
    #include "epix.h"
    using namespace ePiX;

    double rad1(1), rad2(0.75);

    int N(60); // fineness of plot

    // parameter domains for southern/northern portions
    domain lower(P(0, 0, -M_PI_2), P(1, 2*M_PI, 0), mesh(N, N, 0.25*N));
    domain upper(P(0, M_PI_2, 0), P(1, 2*M_PI, M_PI_2), mesh(N, 0.75*N, 0.25*N));

    int main()
    {
      picture(P(-2,-2), P(2,2), "3 x 3in");

      begin();
      camera.at(P(4, 2, 2));

      fill();
      green(0.6);
      scenery S(sph, lower.slice1(rad2));
      S.add(sph, upper.slice1(rad2));

      // add slightly smaller sphere in brighter shade
      double scale(0.99);
      green(1.2);
      S.add(sph, lower.slice1(scale*rad2));
      S.add(sph, upper.slice1(scale*rad2));

      blue(0.8);
      S.add(sph, lower.slice1(rad1));
      S.add(sph, upper.slice1(rad1));

      blue(1.2);
      S.add(sph, lower.slice1(scale*rad1));
      S.add(sph, upper.slice1(scale*rad1));

      S.draw();

      // labels and guide lines
      black();
      P O(0, 0, 0),
        lbl1(sph(1.1*rad1, -M_PI_4, M_PI_4)),
        lbl2(sph(1.2*rad1, -M_PI/8, 5*M_PI/12)),
        lbl2b(sph(rad2, 0, 5*M_PI/12)),
        lbl3(sph(1.2*rad1, M_PI_2, M_PI/3));

      label(lbl1, P(-2, 2), "Outer horizon", tl);
      label(lbl2, P(-2, 2), "Inner horizon", t);
      label(lbl3, P(-2, 2), "Singularity", tr);

      pen(White(), 2);
      line(lbl2, lbl2b);
      line(lbl3, O);

      pen(Black(), 1);
      line(lbl2, lbl2b);
      line(lbl3, O);

      red();
      dot(P(0, 0, 0));

      tikz_format();
      end();
    }

Compilation methods

a)Running ePiX via command line: (Needs an TeXLive distro installed along with ePiX for conversion to pdf)

• Save example code as sphereblack.xp and run at command line elaps --pdf sphereblack.xp generates sphereblack.pdf directly to include in LaTeX separately.

b)Running ePiX inside .tex file :

% pdflatex -shell-escape sphere.tex
\documentclass{article}
\immediate\write18{epix sphereblack.xp} % tikz macros due to tikz_format();
\usepackage{tikz}
\begin{document}
\input{sphereblack.eepic} % Input the tikz macros in sphereblack.eepic
\end{document}

For more detailed information on refer ePiX manual