%% Created by Maple 6 (IBM INTEL NT)
%% Source Worksheet: r-Lequat.mws
%% Generated: Mon Jun 07 21:09:00 2004
%\documentclass{article}
%\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Heading 1}
\DefineParaStyle{Heading 2}
\DefineParaStyle{Heading 3}
\DefineParaStyle{Heading 4}
\DefineParaStyle{Maple Output}
\DefineParaStyle{Warning}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
%\begin{document}
%\pagestyle{empty}
\begin{maplegroup}
\begin{Heading 1}
Kerr black hole
\end{Heading 1}

\begin{Heading 2}
Equatorial plane
\end{Heading 2}

\begin{Heading 3}
Null geodesics
\end{Heading 3}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{restart:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{D_plus := (2*M*a+r*sqrt(r^2-2*M*r+a^2)) /(2*M-r):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{D_minus := (2*M*a-r*sqrt(r^2-2*M*r+a^2)) /(2*M-r):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popt := `portrait, noborder, color`:}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{Heading 4}
Extreme Kerr solution
\end{Heading 4}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{a := M:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M := 1:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(plots):}{%
}
\end{mapleinput}
\vspace{-8mm}
\mapleresult\color{blue}
\begin{maplettyout}
Warning, the name changecoords has been redefined
\end{maplettyout}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plus := plot(D_plus, r = 0..7*M, D = -10..5, discont = 
true, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{minu := plot(D_minus, r = 0..7*M, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis := textplot(\{[2, 4, N], [4, -9, S], [.4, 1.3, W]\},
font = [TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{crit := plot(a, r = 0..7*M, thickness = 1, linestyle = 3,
color = black):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis2 := textplot([0, a, "a"], align = 'LEFT'):}{%
}
\end{mapleinput}

\end{maplegroup}
\bigskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotsetup(ps, plotoutput = `r-Leqext.eps`, plotoptions =
popt):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(plus, minu, popis, thickness = 2, crit, popis2,
title = "r-D plot in the extreme Kerr solution \\n The null
geodesics", titlefont = [TIMES, ROMAN, 15]);}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{Heading 4}
Fast Kerr solution
\end{Heading 4}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{a := 2*.52;}{%
}
\end{mapleinput}

\mapleresult\color{blue}
\begin{maplelatex}
\mapleinline{inert}{2d}{a := 1.04;}{%
\[
a := 1.04
\]
%
}
\end{maplelatex}

\end{maplegroup}
\bigskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plus := plot(D_plus, r = 0..7*M, D = -10..5, discont = 
true, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{minu := plot(D_minus, r = 0..7*M, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis := textplot(\{[2, 4, N], [4, -9, S], [.4, 1.3, W]\},
font = [TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotsetup(ps, plotoutput = `r-Leqfas.eps`, plotoptions =
popt):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(plus, minu, popis, thickness = 2, crit, popis2,
title = "r-D plot in the fast Kerr solution \\n The null
geodesics", titlefont = [TIMES, ROMAN, 15]);}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{Heading 4}
Slow Kerr solution
\end{Heading 4}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{a := 2*.48;}{%
}
\end{mapleinput}

\mapleresult\color{blue}
\begin{maplelatex}
\mapleinline{inert}{2d}{a := .96;}{%
\[
a := .96
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plus := plot(D_plus, r = 0..7*M, D = -10..5, discont =
true):}{%
}
\end{mapleinput}

\end{maplegroup}
\vspace{-7pt}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{minu := plot(D_minus, r = 0..7*M):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis := textplot(\{[2, 4, N], [4, -9, S], [.4, 1.3, W]\},
font = [TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotsetup(ps, plotoutput = `r-Leqslo.eps`, plotoptions =
`portrait, noborder`):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(plus, minu, popis, thickness = 2, crit, popis2,
title = "r-D plot in the slow Kerr solution \\n The null
geodesics", titlefont = [TIMES, ROMAN, 15]);}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
%\end{document}
%% End of Maple 6 Output
