%% Created by Maple 6 (IBM INTEL NT)
%% Source Worksheet: r-Ltimelik.mws
%% Generated: Mon May 03 16:34:46 2004
%\documentclass{article}
%\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Heading 1}
\DefineParaStyle{Heading 2}
\DefineParaStyle{Heading 3}
\DefineParaStyle{Warning}
\DefineCharStyle{2D Comment}
\DefineCharStyle{2D Math}
%\begin{document}
%\pagestyle{empty}
\begin{maplegroup}
\begin{Heading 1}
Kerr space-time
\end{Heading 1}
\nopagebreak[4]
\begin{Heading 2}
\mapleinline{inert}{2d}{r;}{%
$r$%
}-
\mapleinline{inert}{2d}{L;}{%
$L$%
} plot
\end{Heading 2}

\begin{Heading 3}
The time-like 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}{with(plots):}{%
}
\end{mapleinput}

\mapleresult\color{blue}\vspace{-8mm}
\begin{maplettyout}
Warning, the name changecoords has been redefined
\end{maplettyout}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_p :=
plot(1/2*(27*e^2+18*e-1+sqrt((27*e^2+18*e-1)^2+64*e))/e,
e = -1..1.2, Q = -12..32, color = black, labelfont =
[TIMES, ITALIC, 16]):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_m1 :=
plot(1/2*(27*e^2+18*e-1-sqrt((27*e^2+18*e-1)^2+64*e))/e,
e = -1..0, color = black):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_m2 :=
plot(1/2*(27*e^2+18*e-1-sqrt((27*e^2+18*e-1)^2+64*e))/e,
e = 0.2..1.2, color = black):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_m3 :=
plot(1/2*(27*e^2+18*e-1-sqrt((27*e^2+18*e-1)^2+64*e))/e, e
= 0..0.2, color = black, linestyle = 3, numpoints = 12,
adaptive = false):}{%
}
\end{mapleinput}

\end{maplegroup}
\vspace{-5pt}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{a2e := plot( -19*e, e = 0..1.2, color = black):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis := textplot(\{[0.3,20, Q_plus], [-0.2, 24, Q_minus],
[0.8, -2, Q_minus], [0.15, 26, "d > 0"],
[-0.7, 18, "d < 0"], [0.5, 10, "d < 0"], [0.2, -1.7, "d >
0"], [0.9, -6, "d < 0"], [0.9, -10, "Q = -(a^2)e"]\}, font
= [TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis2 := textplot(\{[0, 12, "12M^2"], [0, 16, "16M^2"]\},
align = 'RIGHT'):}{%
}
\end{mapleinput}

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

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display([plotQ_p, plotQ_m1, plotQ_m2, plotQ_m3, a2e,
popis, popis2], thickness = 2, title = "e-Q chart for the
time-like geodesics", titlefont = [TIMES, ROMAN, 15]);}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{Heading 3}
The null geodesis
\end{Heading 3}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Q_null := plot(27*e, e = 0..1.2, Q = -12..32, color =
blue, labelfont = [TIMES, ITALIC, 16]):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{null := textplot(\{[1.2,26, "Q = 27eM^2"], [0.4, 26, "d >
0"], [0.8, 10, "d < 0"], [0.9, -6, "d < 0"], [0.8, -10, "Q
= -(a^2)e"]\}, font = [TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

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

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(Q_null, a2e, null, thickness = 2, title = "e-Q
chart for the null geodesics", titlefont = [TIMES, ROMAN,
15]);}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{Heading 3}
The space-like geodesics
\end{Heading 3}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_ptime :=
plot(1/2*(27*e^2-18*e-1+sqrt((27*e^2-18*e-1)^2-64*e))/e, e
= 1..1.2, Q = -23..23, color = blue, labelfont = [TIMES,
ITALIC, 16], numpoints = 200):}{%
}
\end{mapleinput}

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotQ_m :=
plot(1/2*(27*e^2-18*e-1-sqrt((27*e^2-18*e-1)^2-64*e))/e, e
= 1..1.2, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\vspace{-7pt}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{CI := plot(-19*e, e = 1..1.2, color = black):}{%
}
\end{mapleinput}

\end{maplegroup}
\smallskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis_space := textplot(\{[1.2, 15, Q_plus], [1.2, 4,
Q_minus], [0.8, -2, Q_minus], [1.12, 20, "d > 0"], [1.12,
6, "d < 0"], [1.12, -12, "d < 0"], [1.012, 2, "d > 0"],
[0.9, -6, "d < 0"], [1.2, -20, "Q = -(a^2)e"]\}, font =
[TIMES, BOLDITALIC, 10]):}{%
}
\end{mapleinput}

\end{maplegroup}
\vspace{-6pt}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{popis2_space := textplot([1, 4, "4M^2"], align = 'LEFT'):}{%
}
\end{mapleinput}

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

\end{maplegroup}
\medskip
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(plotQ_ptime, plotQ_m, CI, popis_space,
popis2_space, thickness = 2, title = "e-Q chart for the
space-like geodesics", titlefont = [TIMES, ROMAN, 15]);}{%
}
\end{mapleinput}

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

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