\section{$a/M$ varies}
We start a photon in the equatorial plane, 
$(r,\theta,\varphi)$ = $(5,\pi/2,\pi/4)$, 
and with direction radially inwards, 
$(dr,d\theta,d\varphi)$ = $(-0.5,0,0)$. 
Therefore, it will stay in the equaorial plane.

We integrate the geodesic equation in 300 steps, 
using a step size $d\lambda$ = 0.20

In this movie,
we vary the rotation parameter $a/M$ from 0.00 (no rotation)
to 1.00 (the most extreme rotation possible).
In every frame of the movie, we show a null godesic, that is, the trajectory of
a photon, so it's proper time axis is along the geodesic, so to speak,
and has nothing to do with the time axis of the movie, which shows a change
in $a/M$.

The IDL script is
\linkf{{\tt mf\_01}}
{http://www.astro.ku.dk/\~{}milvang/RelViz/idl/mf\_01.pro}.

\begin{latexonly}
\begin{center}
\fbox{\includegraphics[width=8cm]{Anim/01/a000.ps}}
\end{center}
\end{latexonly}
\begin{rawhtml}
<p>
<center>
<img alt=""
 src="http://www.astro.ku.dk/~milvang/RelViz/Anim/01/a000.gif">
</center>
<p>
\end{rawhtml}
\begin{center} 
\begin{rawhtml}
<center>
\end{rawhtml}
%
Movie: 
\linkf{QuickTime}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a\_over\_M.qt}
      (3.9 Mbyte),
\linkf{MPEG}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a\_over\_M.mpeg}
      (0.5 Mbyte), or
\linkf{animated GIF}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a\_over\_M\_anim.gif}
      (2.2 Mbyte)\\
First frame:
\linkf{Inventor}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a000.iv.gz},
\linkf{VRML}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a000.wrl.gz}, or
\linkf{GIF}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a000.gif}\\
Last frame:
\linkf{Inventor}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a100.iv.gz},
\linkf{VRML}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a100.wrl.gz}, or
\linkf{GIF}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/a100.gif}\\
All files: 
\linkf{this directory}
      {http://www.astro.ku.dk/\~{}milvang/RelViz/Anim/01/}
\end{center}
\begin{rawhtml}
</center>
\end{rawhtml}

{\em Note\/}: this movie has a minor problem:
frame 000 and 001 are identical, except for the annotation text.
This is because something went wrong when running Explorer.
The Inventor (and VRML) files {\em are\/} different.

