[[This is a redo of my "cvs import" of 2002/06/11, this time using proper

cvs operations (commit/delete/add) to preserve the full CVS history of this
thorn.]]

This is a major cleanup/revision of AEIThorns/Exact.

Major user-visible changes:
* major expansion of doc/documentation.tex
* major expansion of documentation in param.ccl file
* add new file describing how to add a new model:  doc/how_to_add_a_new_model
* rename all parameters, systematize spacetime/coordinate/parameter names
  (there is a perl script in par/convert-pars.pl to convert old parameter
  files to the new names)
* [from Mitica Vulcanov] many additions and fixes to
  cosmological solutions and Schwarzschild-Lemaitre
* fix stress-energy tensor computations so they work -- before they were
  all disabled in CVS (INCLUDES lines were commented out in interface.ccl)
  due to requiring excessive friendship with evolution thorns
  and/or public parameters; new code copies parameters to restricted
  grid scalars, which Cactus automagically "pushes" to friends
* added some more tests to testsuite, though these don't yet work fully

Additional internal changes:
* rename many Fortran subroutines (and a few C ones too)
  so their names start with the thorn name
  to reduce the chances of name collisions with other thorns
* move all metrics to subdirectory so the main source directory isn't
  so cluttered
* move two files containing subroutines which were never called
  (they didn't belong in this thorn, but somehow got into cvs by accident)
  into new archive/ directory
* some (small) improvements in efficiency -- the exact_model parameter
  is now decoded from a keyword (string) to an integer once at INITIAL,
  and that integer tested by the stress-energy tensor code,
  rather than requiring a separate series of string tests at each grid
  point (!) like the old stress-energy tensor code did


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinInitialData/Exact/trunk@95 e296648e-0e4f-0410-bd07-d597d9acff87

1 files changed, 848 insertions, 362 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 334f6a2..6e077a7 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -1,98 +1,232 @@
-%version   $Header$
+% *======================================================================*
+%  Cactus Thorn template for ThornGuide documentation
+%  Author: Ian Kelley
+%  Date: Sun Jun 02, 2002
+%  $Header$
+%
+%  Thorn documentation in the latex file doc/documentation.tex 
+%  will be included in ThornGuides built with the Cactus make system.
+%  The scripts employed by the make system automatically include 
+%  pages about variables, parameters and scheduling parsed from the 
+%  relevent thorn CCL files.
+%  
+%  This template contains guidelines which help to assure that your     
+%  documentation will be correctly added to ThornGuides. More 
+%  information is available in the Cactus UsersGuide.
+%                                                    
+%  Guidelines:
+%   - Do not change anything before the line
+%       % BEGIN CACTUS THORNGUIDE",
+%     except for filling in the title, author, date etc. fields.
+%        - Each of these fields should only be on ONE line.
+%        - Author names should be sparated with a \\ or a comma
+%   - You can define your own macros are OK, but they must appear after
+%     the BEGIN CACTUS THORNGUIDE line, and do not redefine standard 
+%     latex commands.
+%   - To avoid name clashes with other thorns, 'labels', 'citations', 
+%     'references', and 'image' names should conform to the following 
+%     convention:          
+%       ARRANGEMENT_THORN_LABEL
+%     For example, an image wave.eps in the arrangement CactusWave and 
+%     thorn WaveToyC should be renamed to CactusWave_WaveToyC_wave.eps
+%   - Graphics should only be included using the graphix package. 
+%     More specifically, with the "includegraphics" command. Do
+%     not specify any graphic file extensions in your .tex file. This 
+%     will allow us (later) to create a PDF version of the ThornGuide
+%     via pdflatex. |
+%   - References should be included with the latex "bibitem" command. 
+%   - use \begin{abstract}...\end{abstract} instead of \abstract{...}
+%   - For the benefit of our Perl scripts, and for future extensions, 
+%     please use simple latex.     
+%
+% *======================================================================* 
+% 
+% Example of including a graphic image:
+%    \begin{figure}[ht]
+% 	\begin{center}
+%    	   \includegraphics[width=6cm]{MyArrangement_MyThorn_MyFigure}
+% 	\end{center}
+% 	\caption{Illustration of this and that}
+% 	\label{MyArrangement_MyThorn_MyLabel}
+%    \end{figure}
+%
+% Example of using a label:
+%   \label{MyArrangement_MyThorn_MyLabel}
+%
+% Example of a citation:
+%    \cite{MyArrangement_MyThorn_Author99}
+%
+% Example of including a reference
+%   \bibitem{MyArrangement_MyThorn_Author99}
+%   {J. Author, {\em The Title of the Book, Journal, or periodical}, 1 (1999), 
+%   1--16. {\tt http://www.nowhere.com/}}
+%
+% *======================================================================* 
+
+% If you are using CVS use this line to give version information
+% $Header$
+
 \documentclass{article}
-\usepackage{amsmath}
+
+% Use the Cactus ThornGuide style file
+% (Automatically used from Cactus distribution, if you have a 
+%  thorn without the Cactus Flesh download this from the Cactus
+%  homepage at www.cactuscode.org)
+\usepackage{../../../../doc/ThornGuide/cactus}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{document}
-\title{Exact}
-\author{Original code by C Gundlach and Miguel Alcubierre, \\
-exact
-solutions added by many other people,	\\
+
+\author{Original code by Carsten Gundlach and Miguel Alcubierre, \\
+        exact solutions added by many other people,	\\
 	this documentation by Jonathan Thornburg}
-%
-% We want CVS to expand the Id keyword on the next line, but we don't
-% want TeX to go into math mode to typeset the expansion (because that
-% wouldn't look as nice in the output), so we use the "$ $" construct
-% to get TeX out of math mode again when typesetting the expansion.
-%
-\date{$ $Id$ $}
+
+% The title of the document (not necessarily the name of the Thorn)
+\title{Thorn Guide for the {\bf Exact} Thorn}
+
+% the date your document was last changed, if your document is in CVS, 
+% please us:
+%    \date{$ $Date$ $}
+\date{$ $Date$ $}
+
 \maketitle
 
-\abstract{
+% Do not delete next line
+% START CACTUS THORNGUIDE
+
+% Add all definitions used in this documentation here 
+%   \def\mydef etc
+
+% force a line break in a itemize/description/enumerate environment
+\def\forcelinebreak{\mbox{}\\[-\baselineskip]}
+
+\def\defn#1{{\bf #1}}
+
+\def\eg{e.g.\hbox{}}
+\def\ie{i.e.\hbox{}}
+\def\etal{{\it et~al.\/\hbox{}}}
+\def\nb{n.b.\hbox{}}
+\def\Nb{N.b.\hbox{}}
+
+% math stuff
+\def\diag{\text{diag}}
+\def\Gaussian{{\sf G}}
+\def\half{{\textstyle \frac{1}{2}}}
+\def\sech{\text{sech}}
+
+% Add an abstract for this thorn's documentation
+\begin{abstract}
 This thorn sets up the $3+1$ ADM field variables for any of a number
 of exact spacetimes/coordinates, and even some non-Einstein
 spcetimes/coordinates.  It's easy to add more spacetimes/coordinates:
 all you have to supply is the 4-metric $g_{ab}$ and the inverse 4-metric
-$g^{ab}$, this thorn automagically calculates all the ADM variables
-from these. Optionally, the ADM variables can be calculated on an
+$g^{ab}$ (this thorn automagically calculates all the ADM variables
+from these). Optionally, the ADM variables can be calculated on an
 arbitrary slice through the spacetime, using arbitrary coordinates on
 the slice. Given a lapse and shift, the slice can be evolved through
 the exact solution, in order to check on an evolution code, or in
 order to test gauge conditions without the need for an evolution code.
-	 }  
+\end{abstract}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Introduction}
 
-This thorn sets up the ADM field variables for any of the following
-spacetimes/coordinates, as specified by the \verb|exact::exactmodel|
-parameter:
+This thorn sets up the ADM field variables for any of a number of
+different spacetimes/coordinates (we call the combination of a
+spacetime and a coordinate system a \defn{model}), as specified by the
+\verb|Exact::exact_model| parameter.
+
+Optionally, the ADM variables can be calculated on an arbitrary slice
+through the spacetime, using arbitrary coordinates on the slice. Given
+a lapse and shift, the slice can be evolved through the exact
+solution, in order to check on an evolution code, or in order to test
+gauge conditions without the need for an evolution code. This is
+documented in the file \verb|slice_evolver.tex| in the \verb|doc/|
+directory.
+
+The following models are currently supported:%%%
+\footnote{%%%
+	 To add a new model, you have to modify a
+	 number of files in this thorn.  See the file
+	 {\tt how\_to\_add\_a\_new\_model} in the
+	 {\tt doc/} directory for a detailed list of
+	 what to do.  Please follow the naming conventions
+	 given in the next subsection.
+	 }%%%
 \begin{description}
-\item[Minkowski spacetime]\mbox{}\\[-\baselineskip]
+\item[Minkowski spacetime]\forcelinebreak
 	\begin{description}
 	\item[{\tt "Minkowski"}]
 		Minkowski spacetime
-	\item[{\tt "flatfunny"}]
+	\item[{\tt "Minkowski/shift"}]
+		Minkowski spacetime with time-dependent shift vector
+	\item[{\tt "Minkowski/funny"}]
 		Minkowski spacetime in non-trivial spatial coordinates
-	\item[{\tt "flatshift"}]
-		Minkowski spacetime in non-trivial slices with shift
+	\item[{\tt "Minkowski/gauge wave"}]
+		Minkowski spacetime in gauge-wave coordinates
 	\end{description}
-\item[Black hole spacetimes]\mbox{}\\[-\baselineskip]
+\item[Black hole spacetimes]\forcelinebreak
 	\begin{description}
-	\item[{\tt "flatSchwarz"}]
-		Schwarzschild spacetime with flat spatial metric
-	\item[{\tt "Novikov"}]
-		Schwarzschild spacetime in Novikov coordinates
-	\item[{\tt "Finkelstein"}]
+	\item[{\tt "Schwarzschild/EF"}]
 		Schwarzschild spacetime in Eddington-Finkelstein coordinates
-	\item[{\tt "Kerr"}]
-		Kerr spacetime in cartesian coordinates
-	\item[{\tt "KerrSchild"}]
+	\item[{\tt "Schwarzschild/PG"}]
+		Schwarzschild spacetime in Painlev\'{e}-Gullstrand coordinates
+		(these have a flat 3-metric)
+	\item[{\tt "Schwarzschild/Novikov"}]
+		Schwarzschild spacetime in Novikov coordinates
+	\item[{\tt "Kerr/Boyer-Lindquist"}]
+		Kerr spacetime in Boyer-Lindquist coordinates
+	\item[{\tt "Kerr/Kerr-Schild"}]
 		Kerr spacetime in Kerr-Schild coordinates
-	\item[{\tt "fakebinary"}]
-		Thorne's ``fake binary'' approximate spacetime
-	\item[{\tt "multiBH"}]
+	\item[{\tt "Schwarzschild-Lemaitre"}]
+		Schwarzschild-Lemaitre spacetime
+		(Schwarzschild black hole with a cosmological constant)
+	\item[{\tt "multi-BH"}]
 		Majumdar-Papapetrou or Kastor-Traschen
-		maximally-charged multi-BH solutions
+		maximally-charged (extreme Reissner-Nordstrom)
+		multi-BH solutions
+	\item[{\tt "Alvi"}]
+		Alvi post-Newtonian 2BH spacetime (not fully implemented yet)
+	\item[{\tt "Thorne-fakebinary"}]
+		Thorne's ``fake binary'' spacetime (non-Einstein)
 	\end{description}
-\item[Cosmological spacetimes]\mbox{}\\[-\baselineskip]
+\item[Cosmological spacetimes]\forcelinebreak
 	\begin{description}
-	\item[{\tt "Rob-Wal"}]
-		Pure-radiation Robertson-Walker cosmology
-	\item[{\tt "DeSitter"}]
-		Einstein-De~Sitter spacetime
-	\item[{\tt "Godel"}]
-		G\"{o}del spacetime%%%
-\footnote{%%%
-	 Note that the parameter is {\em not\/} "Goedel"!
-	 }%%%
-	\item[{\tt "BianchiI"}]
-		Approximate Bianchi type~I spacetime
+	\item[{\tt "Lemaitre"}]
+		Lemaitre-type spacetime
+	\item[{\tt "Robertson-Walker"}]
+		Robertson-Walker spacetime
+	\item[{\tt "de Sitter"}]
+		de~Sitter spacetime
+	\item[{\tt "de Sitter+Lambda"}]
+		de~Sitter spacetime with cosmological constant
+	\item[{\tt "anti-de Sitter+Lambda"}]
+		anti-de~Sitter spacetime with cosmological constant
+	\item[{\tt "Bianchi I"}]
+		approximate Bianchi type~I spacetime
+	\item[{\tt "Goedel"}]
+		G\"{o}del spacetime
+	\item[{\tt "Bertotti"}]
+		Bertotti spacetime
 	\item[{\tt "Kasner"}]
 		Kasner-like spacetime
+	\item[{\tt "Kasner-axisymmetric"}]
+		axisymmetric Kasner spacetime
+	\item[{\tt "Kasner-generalized"}]
+		generalized Kasner spacetime
 	\item[{\tt "Milne"}]
 		Milne spacetime for pre-big-bang cosmology
 	\end{description}
-\item[Miscellaneous spacetimes]\mbox{}\\[-\baselineskip]
+\item[Miscellaneous spacetimes]\forcelinebreak
 	\begin{description}
-	\item[{\tt "boostrot"}]
-		Boost-rotation symmetric spacetime
-	\item[{\tt "starSchwarz"}]
-		Schwarzschild (constant density) star
+	\item[{\tt "boost-rotation symmetric"}]
+		boost-rotation symmetric spacetime
 	\item[{\tt "bowl"}]
-		Non-Einstein Bowl (``bag of gold'') spacetime
+		bowl (``bag of gold'') spacetime (non-Einstein)
+	\item[{\tt "constant density star"}]
+		constant density (Schwarzschild) star
 	\end{description}
 \end{description}
 
@@ -102,12 +236,75 @@ with that if needed) is known throughout the spacetime.  Cases where
 this is only known on one specific slice, should live in separate
 initial data thorns.
 
-Optionally, the ADM variables can be calculated on an arbitrary slice
-through the spacetime, using arbitrary coordinates on the slice. Given
-a lapse and shift, the slice can be evolved through the exact
-solution, in order to check on an evolution code, or in order to test
-gauge conditions without the need for an evolution code. This is
-documented in slice\_evolver.tex (which you should find in Exact/doc).
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Naming Conventions}
+
+This thorn includes many different spacetimes and coordinate systems,
+so we use the following naming conventions to help keep the different
+models and parameters clear:
+\begin{itemize}
+\item	If we have multiple coordinate systems for a given spacetime,
+	the models are named with the pattern
+	\hbox{{\tt "}spacetime{\tt /}coordinates{\tt "}}.
+	For example, the model \verb|"Schwarzschild/EF"| is Schwarzschild
+	spacetime in Eddington-Finkelstein coordinates.%%%
+\footnote{%%%
+	 We abbreviate the coordinate names both for
+	 convenience, and because the unabbreviated
+	 names would make the variable names in the
+	 code (which are the same as the parameter names)
+	 too long -- C only guarantees 31~characters for
+	 variable names, and the Fortran~95 standard
+	 explicitly limits variable names to this same
+	 maximum length.
+	 }%%%
+\item	If we have spacetimes which are identical or very similar,
+	except that one has a cosmological constant and the other
+	doesn't, we name the with-cosmological-constant one by appending
+	\verb|+Lambda| to the without-cosmological-constant spacetime
+	name.  For example, the cosmological-constant variant of
+	anti-de Sitter spacetime is the model \verb|"anti-de Sitter+Lambda"|.
+\item	All the parameters for individual models have names which begin
+	with the model name (with any slash (\verb|/|) or hyphen (\verb|-|)
+	characters converted to underscores (\verb|_|)), followed by
+	a double underscore (\verb|__|).
+\item	The description comment for each parameter in the \verb|param.ccl|
+	file begins with the model name follwed by a colon (\verb|:|).
+	For example,
+\begin{verbatim}
+REAL Schwarzschild_EF__mass "Schwarzschild/EF: BH mass"
+{
+*:* :: "any real number"
+} 1.0
+\end{verbatim}
+\end{itemize}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{The Cosmological Constant and the Stress-Energy Tensor}
+
+A number of these models have a cosmological constant.  To use these
+with the Cactus code (which generally is written for the case of no
+cosmological constant), we use a simple trick: we transfer the term
+with the cosmological constant to the right hand side of the Einstein
+equations, introducing fictitious ``matter'' terms in the stress-energy 
+tensor.
+
+This thorn uses the standard Cactus ``\verb|CalcTmunu|'' interface
+for introducing terms into the stress-energy tensor.  See Ian Hawke's
+documentation for the {\bf ADMCoupling} thorn for details.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Further Sources of Information}
+
+This documentation is a best a secondary source of information about
+this thorn -- the primary sources are the \verb|param.ccl| file and
+the source code itself.  In particular, much of this documentation
+was developed by reverse-engineering from these primary sources, so
+it's quite possible (indeed even likely!) that there are errors or
+omissions here.  Caveat Lector!
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -120,11 +317,10 @@ types of coordinates:
 
 \subsection{Minkowski Spacetime}
 
-\verb|Exact::exactmodel = "Minkowski"| specifies Minkowski spacetime
+\verb|Exact::exact_model = "Minkowski"| specifies Minkowski spacetime
 in the usual Minkowski coordinates:
 \begin{equation}
-g_{ab} = \text{diag}
-	 \left[
+g_{ab} = \diag \left[
 	 \begin{array}{cccc}
 	 -1	& 1	& 1	& 1	%%%\\
 	 \end{array}
@@ -133,153 +329,152 @@ g_{ab} = \text{diag}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Minkowski Spacetime in Non-Trivial Spatial Coordinates}
+\subsection{Minkowski Spacetime in Non-Trivial Spatial coordinates}
 
-\verb|Exact::exactmodel = "flatfunny"| specifies Minkowski spacetime
+\verb|Exact::exact_model = "Minkowski/funny"| specifies Minkowski spacetime
 with the usual Minkowski time slicing, but using the nontrivial spatial
 coordinates defined as follows:  First take the flat metric in polar
 spherical coordinates, then define a new radial coordinate by
 \begin{equation}
-r = r_\text{new} (1 - a {\sf G}(r_\text{new}))
+r = r_\text{new} \big(1 - a \Gaussian(r_\text{new})\big)
 \end{equation}
-where $a = \verb|Exact::flatfunny_a|$ is a specified parameter with
-$a \in [0,1)$, and ${\sf G}(r) = \exp(-\frac{1}{2} r^2/\sigma^2)$
-is a Gaussian centered at $r=0$ with amplitude~1 and width
-$\sigma = \verb|Exact::flatfunny_s|$.  Finally, transform back to
-Cartesian coordinates.
+where 
+$\Gaussian(r) = \exp(-\half r^2/\sigma^2)$ is a Gaussian centered at $r=0$.
+
+The parameters are the perturbation amplitude
+$a = \verb|Exact::Minkowski_funny__amplitude|$
+and the perturbation width $\sigma = \verb|Exact::Minkowski_funny__sigma|$.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Minkowski Spacetime in Non-Trivial Slices with Shift}
 
-\verb|Exact::exactmodel = "flatshift"| specifies Minkowski spacetime
+\verb|Exact::exact_model = "Minkowski/shift"| specifies Minkowski spacetime
 with the nontrivial time slicing and spatial coordinates defined as
 follows:  First take the flat 4-metric in polar spherical coordinates,
 then define a new time coordinate by
 \begin{equation}
-t_\text{new} = t - a {\sf G}(r)
+t_\text{new} = t - a \Gaussian(r)
 \end{equation}
-where $a = \verb|Exact::flatshift_a|$ is a specified parameter with
-$a \in (-1,1)$, and ${\sf G}(r) = \exp(-\frac{1}{2} r^2/\sigma^2)$
-is a Gaussian centered at $r=0$ with amplitude~1 and width
-$\sigma = \verb|Exact::flatshift_s|$.  Finally, transform back to
-Cartesian (4-)coordinates.  (N.b.\ this gives a time-independent
-4-metric.)
+$\Gaussian(r) = \exp(-\half r^2/\sigma^2)$ is a Gaussian centered at $r=0$.
+Note this gives a time-indpendent 4-metric.
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\section{Black Hole Spacetimes}
-
-This thorn can set up Schwarzschild, Kerr, and even some other types
-of black hole or pseudo-black-hole spacetimes, using several different
-types of coordinates:
+The parameters are the perturbation amplitude
+$a = \verb|Exact::Minkowski_shift__amplitude|$
+and the perturbation width $\sigma = \verb|Exact::Minkowski_shift__sigma|$.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Schwarzschild Spacetime with Flat Spatial Metric}
+\subsection{Minkowski Spacetime in gauge-wave coordinates}
 
-\verb|Exact::exactmodel = "flatSchwarz"| specifies Schwarzschild spacetime
-in Painleve-Gustrand coordinates (these have a {\em flat\/} 3-metric),
-transformed to the usual Cactus $(t,x,y,z)$ Cartesian-topology
-coordinates.  The only physics parameter is
+\verb|Exact::exact_model = "Minkowski/gauge wave"| specifies Minkowski
+spacetime with the ``gauge-wave'' coordinates suggested by Carlos Bona:
+The line element is
 \begin{equation}
-m = \text{\tt KerrSchild\_m}
+ds^2=-H dt^2 +Hdx^2+dy^2+dz^2,
 \end{equation}
-(note the name!).
-There is also a numerical parameter \verb|KerrSchild_eps| (again note
-the name!) which is used to avoid division by zero if a grid point falls
-exactly at the origin; the default setting should be ok for most purposes.
+where $H=H(x-t)$, for instance $H=1-a*\sin\big((x-t)/d\big)$.
+This is flat space but the slice is a planar wave travelling along the x axis.
+
+This thorn implements several possible choices for the $H$ function,
+controlled by the \verb|Minkowski_gauge_wave__what_fn| parameter:
+\begin{eqnarray}
+H(x-t)	&=& 1- A \sin \left(\frac{x-t}{d}\right)			\\
+H(x-t)	&=& \exp \left(A*sin(x)*cos(x)\right)				\\
+H(x-t)	&=& 1- A exp(-x^2)						%%%\\
+\end{eqnarray}
+The parameters are
+\begin{itemize}
+\item	$A = \verb|Minkowski_gauge_wave__amplitude|$, the amplitude
+\item	$\omega = \verb|Minkowski_gauge_wave__omega|$, the angular frequency
+\item	$\lambda = \verb|Minkowski_gauge_wave__lambda|$, the wavelength
+\item	$\delta = \verb|Minkowski_gauge_wave__phase|$, the phase shift
+\end{itemize}
+Unfortunately, you have to look at the source code to see exactly what
+these do. :(
+FIXME: someone reverse-engineer the code and change the equations above
+to match whatever the code actually does.
+
+If the Boolean parameter \verb|Minkowski_gauge_wave__diagonal| is true,
+then we make the gauge wave travel diagonally across the grid by the
+coordinate transformation
+\begin{eqnarray}
+x &=& \frac{1}{\sqrt{2}}(x^\prime - y^\prime)				\\
+y &=& \frac{1}{\sqrt{2}}(x^\prime + y^\prime)				%%%\\
+\end{eqnarray}
+For code testing, the idea is to test evolving this with periodic boundary
+conditions, to see whether the code is able to cope with that.
+The tricky part is to make the wave fit the grid exactly (otherwise the
+periodic boundary wouldn't make sence), especially in the diagonal case.
 
-In the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates, the
-4-metric is
-\begin{equation}
-g_{ab} = \left[
-	 \begin{array}{cccc}
-	 -1 + \frac{2m}{r}
-		& \sqrt{\frac{2m}{r}} \frac{x}{r}
-			& \sqrt{\frac{2m}{r}} \frac{y}{r}
-				& \sqrt{\frac{2m}{r}} \frac{z}{r}
-									\\
-	 \sqrt{\frac{2m}{r}} \frac{x}{r}
-		& 1	& 0	& 0					\\
-	 \sqrt{\frac{2m}{r}} \frac{y}{r}
-		& 0	& 1	& 0					\\
-	 \sqrt{\frac{2m}{r}} \frac{z}{r}
-		& 0	& 0	& 1					%%%\\
-	 \end{array}
-	 \right]
-\end{equation}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Black Hole Spacetimes}
 
-\subsection{Schwarzschild Spacetime in Novikov Coordinates}
-
-\verb|Exact::exactmodel = "Novikov"| specifies the unit-mass Schwarzschild
-spacetime in Novikov coordinates, as described in gr-qc/9608050
-(see also MTW section~31.4 and figure~31.2), transformed to the
-usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates.  There are
-no parameters.
+This thorn can set up Schwarzschild and Kerr spacetimes in several
+different types of coordinates, and also a couple of multiple-black-hole
+spacetimes:
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Schwarzschild Spacetime in Eddington-Finkelstein Coordinates}
+\subsection{Schwarzschild Spacetime in Eddington-Finkelstein coordinates}
 
-\verb|Exact::exactmodel = "Finkelstein"| specifies Schwarzschild spacetime
-in (ingoing) Eddington-Finkelstein coordinates $(t,r,\theta,\phi)$, as
-described in MTW box~31.2 and figure~32.1 (that is, $r$ is the usual
-areal radial coordinate, and $t+r$ is an ingoing null coordinate),
-but transformed to the usual Cactus $(t,x,y,z)$ Cartesian-topology
-coordinates.  The only physics parameter is
-\begin{equation}
-m = \text{\tt KerrSchild\_m}
-\end{equation}
-(note the name!).
-There is also a numerical parameter \verb|KerrSchild_eps| (again note
-the name!) which is used to avoid division by zero if a grid point falls
-exactly at the origin; the default setting should be ok for most purposes.
+\verb|Exact::exact_model = "Schwarzschild/EF"| specifies Schwarzschild
+spacetime in (ingoing) Eddington-Finkelstein coordinates, as described
+in MTW box~31.2 and figure~32.1.  The only physics parameter is
+the black hole mass $m = \verb|Schwarzschild_EF__mass|$.
+
+There is also a numerical parameter \verb|Schwarzschild_EF__epsilon|
+which is used to avoid division by zero if a grid point falls exactly
+at the origin; the default setting should be ok for most purposes.
 
 In the usual polar spherical $(t,r,\theta,\phi)$ coordinates, the 4-metric
 and ADM variables are
-\begin{align}
-g_{ab} & = \left[
-	   \begin{array}{cccc}
-	   - \left( 1 - \frac{2m}{r} \right)
+\begin{eqnarray}
+g_{ab}	& = &
+	\left[
+	 \begin{array}{cccc}
+	 - \left( 1 - \frac{2m}{r} \right)
 			& \frac{2m}{r}	& 0	& 0	\\
-	   \frac{2m}{r}	& 1 + \frac{2m}{r}
+	 \frac{2m}{r}	& 1 + \frac{2m}{r}
 					& 0	& 0	\\
-	   0		& 0		& r^2	& 0	\\
-	   0		& 0		& 0	& r^2 \sin^2 \theta
+	 0		& 0		& r^2	& 0	\\
+	 0		& 0		& 0	& r^2 \sin^2 \theta
 							%%%\\
-	   \end{array}
-	   \right]
+	 \end{array}
+	 \right]
 									\\
-g_{ij} & = \text{diag}
-	   \left[
-	   \begin{array}{ccc}
-	   1 + \frac{2m}{r}	& r^2	& r^2 \sin^2 \theta	%%%\\
-	   \end{array}
-	   \right]
+g_{ij}	& = &
+	\diag
+	\left[
+	\begin{array}{ccc}
+	1 + \frac{2m}{r}	& r^2	& r^2 \sin^2 \theta	%%%\\
+	\end{array}
+	\right]
 									\\
-K_{ij} & = \text{diag}
-	   \left[
-	   \begin{array}{ccc}
-	   - \frac{2m^2}{r^2} \frac {1 + \frac{m}{r}} {\sqrt{1 + \frac{2m}{r}}}
+K_{ij}	& = &
+	\diag
+	\left[
+	\begin{array}{ccc}
+	- \frac{2m^2}{r^2} \frac {1 + \frac{m}{r}} {\sqrt{1 + \frac{2m}{r}}}
 				& \frac{2m^2}{\sqrt{1 + \frac{2m}{r}}}
 					& \frac{2m^2}{\sqrt{1 + \frac{2m}{r}}}
 					  \sin^2 \theta		%%%\\
-	   \end{array}
-	   \right]
+	\end{array}
+	\right]
 									\\
-\alpha & = \frac{1}{\sqrt{1 + \frac{2m}{r}}}
+\alpha	& = &
+	\frac{1}{\sqrt{1 + \frac{2m}{r}}}
 									\\
-\beta^i& = \left[
-	   \begin{array}{ccc}
-	   \frac{2m}{r} \frac{1}{\sqrt{1 + \frac{2m}{r}}}
+\beta^i	& = &
+	\left[
+	\begin{array}{ccc}
+	\frac{2m}{r} \frac{1}{\sqrt{1 + \frac{2m}{r}}}
 				& 0	& 0			%%%\\
-	   \end{array}
-	   \right]
+	\end{array}
+	\right]
 									%%%\\
-\end{align}
+\end{eqnarray}
 (Various other $3+1$ variables for Schwarzschild spacetime in these
 coordinates are tabulated in appendix~2 of Jonathan Thornburg's Ph.D
 thesis, \verb|http://www.aei.mpg.de/~jthorn/phd/html/phd.html|.)
@@ -311,44 +506,98 @@ g_{ab} = \left[
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Kerr Spacetime in Cartesian Coordinates}
+\subsection{Schwarzschild spacetime in Painlev\'{e}-Gullstrand coordinates}
+
+\verb|Exact::exact_model = "Schwarzschild/PG"| specifies Schwarzschild
+spacetime in Painlev\'{e}-Gullstrand coordinates, as described by
+Martel and Poisson, gr-qc/0001069.  These coordinates have the
+interesting property that the spatial metric is {\em flat\/}.
+The only physics parameter is the black hole mass
+$m = \verb|Schwarzschild_PG__mass|$.
+
+There is also a numerical parameter \verb|Schwarzschild_PG__epsilon|
+which is used to avoid division by zero if a grid point falls exactly
+at the origin; the default setting should be ok for most purposes.
+
+In the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates, the
+4-metric is
+\begin{equation}
+g_{ab} = \left[
+	 \begin{array}{cccc}
+	 -1 + \frac{2m}{r}
+		& \sqrt{\frac{2m}{r}} \frac{x}{r}
+			& \sqrt{\frac{2m}{r}} \frac{y}{r}
+				& \sqrt{\frac{2m}{r}} \frac{z}{r}
+									\\
+	 \sqrt{\frac{2m}{r}} \frac{x}{r}
+		& 1	& 0	& 0					\\
+	 \sqrt{\frac{2m}{r}} \frac{y}{r}
+		& 0	& 1	& 0					\\
+	 \sqrt{\frac{2m}{r}} \frac{z}{r}
+		& 0	& 0	& 1					%%%\\
+	 \end{array}
+	 \right]
+\end{equation}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Schwarzschild Spacetime in Novikov coordinates}
 
-\verb|Exact::exactmodel = "Kerr"| specifies Kerr spacetime in
-FIXME coordinates.
+\verb|Exact::exact_model = "Novikov"| specifies the unit-mass Schwarzschild
+spacetime in Novikov coordinates, as described in gr-qc/9608050
+(see also MTW section~31.4 and figure~31.2).
+The only physics parameter is the black hole mass
+$m = \verb|Schwarzschild_Novikov__mass|$.
 
-FIXME: more detail needed from Mitica
+There is also a numerical parameter \verb|Schwarzschild_Novikov__epsilon|
+which is used to avoid division by zero if a grid point falls exactly
+at the origin; the default setting should be ok for most purposes.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Kerr Spacetime in Boyer-Lindquist coordinates}
+
+\verb|Exact::exact_model = "Kerr/Boyer-Lindquist"| specifies Kerr
+spacetime in (cartesian) Boyer-Lindquist coordinates, as described
+in MTW box~33.2.  The physics parameters are
+the black hole mass $m = \verb|Kerr_BoyerLindquist__mass|$, and the
+dimensionless spin parameter $a = J/m^2 = \verb|Kerr_BoyerLindquist__spin|$.
+
+Mitica Vulcanov says: this metric still need some work in order to
+run properly. Major problems: the convergence and calibration of the
+units for the parameters and variables.  
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Kerr-Schild form of Boosted Rotating Black Hole}
 
-\verb|Exact::exactmodel = "KerrSchild"| specifies Kerr spacetime in
+\verb|Exact::exact_model = "KerrSchild"| specifies Kerr spacetime in
 Kerr-Schild coordinates, as described in MTW exercise~33.8, Lorentz
 boosted in the $z$ direction so the black hole is centered at the
-position $z = vt$, and transformed to the usual Cactus $(t,x,y,z)$
-Cartesian-topology coordinates.  The physics parameters are
-\begin{align}
-a & = \text{\tt KerrSchild\_a}						\\
-m & = \text{\tt KerrSchild\_m}						\\
-v & = \text{\tt KerrSchild\_boostv}					%%%\\
-\end{align}
-There is also a numerical parameter \verb|KerrSchild_eps| which is
-used to avoid division by zero if a grid point falls exactly at the
-black hole center; the default setting should be ok for most purposes.
-
-Kerr-Schild coordinates use the same time slicing (n.b.\ non-maximal!)
-and $z$~spatial coordinate as Kerr coordinates, but define new spatial
-coordinates $x$ and~$y$ by
-\begin{equation}
-x + iy = (r + ia) e^{i\phi} \sin\theta
+position $z = vt$.  The physics parameters are
+the black hole mass $m = \verb|Kerr_KerrSchild__m|$, the
+dimensionless spin parameter $a = J/m^2 = \verb|Kerr_KerrSchild__spin|$,
+and the boost velocity $v = \verb|Kerr_KerrSchild__boost_v|$.
+
+There is also a numerical parameter \verb|Kerr_KerrSchild__epsilon|
+which is used to avoid division by zero if a grid point falls exactly
+at the black hole center; the default setting should be ok for most
+purposes.
+
+Kerr-Schild coordinates use the same time slicing (\nb{} non-maximal!)
+and $z$~spatial coordinate as Kerr coordinates $(x_K, y_K, z_K)$, but
+define new spatial coordinates $x \equiv x_{KS}$ and~$y \equiv y_{KS}$
+by
+\begin{equation}
+x_{KS} + iy_{KS} = (r + ia) e^{i\phi} \sin\theta
 \end{equation}
 so that
-\begin{align}
-x	& = x_\text{Kerr} - a \sin\theta \sin\phi			\\
-y	& = y_\text{Kerr} + a \sin\theta \cos\phi			%%%\\
-\end{align}
+\begin{eqnarray}
+x_{KS}	& = & x_K - a \sin\theta \sin\phi				\\
+y_{KS}	& = & y_K + a \sin\theta \cos\phi				%%%\\
+\end{eqnarray}
 
-In these coordinates the 4-metric can be written
+In Kerr-Schild coordinates the 4-metric can be written
 \begin{equation}
 g_{ab} = \eta_{ab} + 2 H k_a k_b
 \end{equation}
@@ -366,49 +615,73 @@ is a null vector.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Thorne's ``Fake Binary'' Approximate Spacetime}
+\subsection{Schwarzschild-Lemaitre spacetime
+	    (Schwarzschild black hole with cosmological constant}
+
+\verb|Exact::exact_model = "Schwarzschild/Lemaitre"|%%%
+is a metric proposed by Lemaitre in 1932 as a version of the
+Schwarzschild solution in a universe with cosmological constant.
+For a history of this metric and a good review see the chapter of
+Jean Eisenstaedt, ``Lemaitre and the Schwarzschild solution'' in the
+book ``The attraction of Gravitation: New Studies in the History of
+General Relativity'', by J.~Earman, et.al.  Birk\"{a}user, 1993.
+The line element is 
+\begin{equation}
+ds^2 = - \left( 1-\frac{2m}{r} - \frac{\Lambda}{3}r^2\right) \, dt^2
+       + \left( 1-\frac{2m}{r} -\frac{\Lambda}{3}r^2 \right)^{-1} \, dr^2
+       + r^2 \, d\theta^2
+       + r^2 \sin(\theta)^2 \, d\phi^2
+\end{equation}
+Notice that for $\Lambda = 0$ this reduces to Schwarzschild spacetime
+in the usual Schwarzschild coordinates.
 
-\verb|Exact::exactmodel = "fakebinary"| specifies Thorne's ``fake binary''
-approximate spacetime, as described in gr-qc/9808024.  This is not an
-exact solution of the Einstein equations, but has qualitative features
-designed to mimic those of an inspiralling binary black hole spacetime.
-The physics parameters are
-\begin{align}
-m	& = \text{\tt fakebinary\_m}					\\
-a_0	& = \text{\tt fakebinary\_a0}					\\
-\Omega_0& = \text{\tt fakebinary\_Omega0}				%%%\\
-\end{align}
-There are also algorithm parameters \verb|fakebinary_atype|,
-\verb|fakebinary_retarded|, and \verb|fakebinary_bround|.
-There is also a numerical parameter \verb|fakebinary_eps| which is
-used to avoid division by zero if a grid point falls exactly at either
-black hole's center; the default setting should be ok for most purposes.
+The physics parameters are the black hole mass
+$m = \verb|Schwarzschild_Lemaitre__mass|$, and the
+cosmological constant $\Lambda = \verb|Schwarzschild_Lemaitre__Lambda|$.
+
+The fictitious ``matter'' stress-energy tensor representing $\Lambda$ is
+\begin{equation}
+T_{ij}= - \frac{\Lambda}{8 \pi} g_{ij}
+      = \left(
+	\begin{array}{cccc}
+	-\frac{1}{24}\frac{\Lambda A}{r\pi} & 0 & 0 & 0\\
+	0 & \frac{3}{8}\frac{r\Lambda}{8\pi A }& 0 & 0\\
+	0 & 0 &-\frac{1}{8}\frac{\Lambda r^2}{\pi }&  0\\
+	0 & 0 & 0 & -\frac{1}{8}\frac{\Lambda r^2 \sin(\theta)^2}{\pi}
+	\end{array}
+	\right)
+\end{equation}
+where $A = (-3r +6m+\Lambda r^3)$.
+
+Alas, this metric doesn't seem to give proper finite difference
+convergence for $\Lambda \ne 0$.  It works fine for $\Lambda = 0$.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Majumdar-Papapetrou or Kastor-Traschen
-	    Maximally-Charged multi-BH Solutions}
+	    Maximally-Charged (extreme Reissner-Nordstrom) multi-BH Solutions}
 
-\verb|Exact::exactmodel = "multiBH"| specifies the Majumdar-Papapetrou
+\verb|Exact::exact_model = "multi-BH"| specifies the Majumdar-Papapetrou
 or Kastor-Traschen solution.  The file \verb|KTsol.tex| in the
 documentation directory of this thorn gives more details/references
 about these solutions.
 
 The Majumdar-Papapetrou solution is a multi-black-hole static solution
-to Einstein's equation, containing $N$ maximally charged ($Q=M$) black
-holes.  The balance between gravitational attraction and electrostatic
-repulsion among the black holes causes each to maintain its position
-relative to the others eternally.  (The Majumdar-Papapetrou solution
-somewhat resembles Brill-Lindquist initial data, but with the black
-holes being charged to make the solution static.)  The line element is
+to Einstein's equation, containing $N$ maximally charged ($Q=M$, \ie{}
+extreme Reissner-Nordstrom) black holes.  The balance between
+gravitational attraction and electrostatic repulsion among the
+black holes causes each to maintain its position relative to the
+others eternally, so the spacetime is static.  (The Majumdar-Papapetrou
+solution somewhat resembles Brill-Lindquist initial data, but with the
+black holes being charged.)  The line element is
 \begin{equation}
 ds^2=-\frac{1}{\Omega^2} dt^2+ \Omega^2(dx^2+dy^2+dz^2)
 \end{equation}
 where
-\begin{align}
-\Omega	&= 1+\sum_{i=1}^N \frac{M_i}{r_i}				\\
-r_i	&= \sqrt{(x-x_i)^2+(y-y_i)^2+(z-z_i)^2}				%%%\\
-\end{align}
+\begin{eqnarray}
+\Omega	&=& 1+\sum_{i=1}^N \frac{M_i}{r_i}				\\
+r_i	&=& \sqrt{(x-x_i)^2+(y-y_i)^2+(z-z_i)^2}				%%%\\
+\end{eqnarray}
 where $M_i$ and $(x_i, y_i, z_i) \in \Re^3$ are the masses and
 locations of the individual black holes.
 
@@ -423,81 +696,163 @@ The Kastor-Traschen line element is
 ds^2=-\frac{1}{\Omega^2} dt^2+a(t)^2 \Omega^2(dx^2+dy^2+dz^2)
 \end{equation}
 where
-\begin{align}
-\Omega	&= 1+\sum_{i=1}^N {\frac{M_i}{a r_i}}				\\
-a	&= e^{Ht}							\\
-H	&= \pm \sqrt{\frac{\Lambda}{3}}					\\
-r_i	&= \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2}			%%%\\
-\end{align}
+\begin{eqnarray}
+\Omega	&=& 1+\sum_{i=1}^N {\frac{M_i}{a r_i}}				\\
+a	&=& e^{Ht}							\\
+H	&=& \pm \sqrt{\frac{\Lambda}{3}}				\\
+r_i	&=& \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2}			%%%\\
+\end{eqnarray}
 This solution represents ``incoming'' (``outgoing'') charged BHs
 if $H < 0$ ($H > 0$).  We interpret $M_i$ as the mass of the
 $i{\rm th}$ black hole, although we have neither an asymptotically
 flat region nor event horizons available to convert this naive
 interpretation into a rigorous one.
 
-This thorn supports up to 4~black holes; the physics parameters are
-\begin{align}
-N	& = \text{\tt KT\_nBH}						\\
-H	& = \text{\tt KT\_Hubble}					%%%\\
-\end{align}
-and
-\begin{align}
-M_i	& = \text{\tt m\_bh$i$}						\\
-x_i	& = \text{\tt co\_bh$i$x}					\\
-y_i	& = \text{\tt co\_bh$i$y}					\\
-z_i	& = \text{\tt co\_bh$i$z}					%%%\\
-\end{align}
-for each $i = 1$, $2$, $3$, $4$.
+This thorn supports up to 4~black holes.  The physics parameters are
+the number of black holes $N = \verb|multi_BH__nBH|$ and the Hubble constant
+$H = \verb|multi_BH__Hubble|$, and then for each black hole $i = 1, \dots, N$,
+the mass $m_i = \verb|multi_BH__mass|\,i$ and the $x$, $y$, and $z$ positions
+$x_i = \verb|multi_BH__x|\,i$, $y_i = \verb|multi_BH__y|\,i$,
+and $z_i = \verb|multi_BH__z|\,i$ respectively.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Alvi post-Newtonian 2BH spacetime (not fully implemented yet)}
+
+\verb|Exact::exact_model = "Alvi"| specifies the Alvi post-Newtonian
+binary black hole metric, as described in gr-qc/9912113.  This
+uses different approxamintion methods to describe different regions
+of a binary black hole system: Near the holes, one uses a distorted
+Schwarzschild black hole metric, while in the region around them
+(divided into a near zone and a wave zone) one uses a 1st~order
+post-Newtonian approximation. There are discontinuities at the
+boundaries between the zones. 
+
+This model has physics parameters giving the masses of the two black
+holes, $m_1 = \verb|Alvi__mass1|$ and $m_2 = \verb|Alvi__mass2|$, and
+their spatial separation $b = \verb|Alvi__separation|$.
+
+Unfortunately, this metric isn't fully implemented yet.
+See Nina Jansen for details.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Thorne's ``Fake Binary'' Approximate Spacetime}
+
+\verb|Exact::exact_model = "fakebinary"| specifies Thorne's ``fake binary''
+approximate binary-black-hole spacetime, as described in gr-qc/9808024.
+This is not an exact solution of the Einstein equations, but has
+qualitative features designed to mimic those of an inspiralling
+binary black hole spacetime.  The physics parameters are:
+\begin{itemize}
+\item	$m = \verb|Thorne_fakebinary__mass|$, the mass\\
+	(FIXME: is this the mass of the whole spacetime,
+	or of an individual BH?)
+\item	$a_0 = \verb|Thorne_fakebinary__separation|$, the initial binary
+	separation
+\item	$\Omega_0 = \verb|Thorne_fakebinary__Omega0|$, the initial
+	angular frequency of the binary orbit
+\item	\verb|Thorne_fakebinary__retarded|, a Boolean parameter which
+	controls whether or not to use a retarded time coordinate
+\item	\verb|Thorne_fakebinary__atype|, a keyword parameter to
+	select a constant (\verb|"constant"|)
+	or quadrupole (\verb|"quadrupole"|) solution
+\item	\verb|Thorne_fakebinary__smoothing|, a smoothing length for
+	the Newtonian potential
+\end{itemize}
+
+There is also a numerical parameter \verb|Thorne_fakebinary__epsilon|
+which is used to avoid division by zero if a grid point falls exactly
+at either black hole's center; the default setting should be ok for
+most purposes.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Cosmological Spacetimes}
 
+The code for most of these models was written by
+Mitica Vulcanov \verb|<vulcan@aei.mpg.de>|.
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Pure-Radiation Robertson-Walker Cosmology}
+\subsection{Lemaitre-type spacetime}
+
+\verb|Exact::exact_model="Lemaitre"| specifies a Lemairre spacetime,
+version of the Friedmann-Robertson-Walker model with flat space
+(\ie{} $k=0$), possibly a cosmological constant, $\Lambda$, and a
+linear dependence between the energy density $\epsilon$ and the
+pressure, $p$, namely $p=\kappa \epsilon$. Thus the metric is the
+Robertson-Walker metric
+(see section~\ref{AEIThorns/Exact/sect-Robertson-Walker}) with
+$k =0$ and (see gr-qc/0110030, astro-ph/9910093 and references cited here)
+\begin{equation}
+R(t) = R_0 \left[ \cosh \left(\frac{\sqrt{3\Lambda}}{2}(\kappa+1) t \right)
+		  +
+		  \sqrt{1+\frac{8\pi G\,\epsilon_{0}}{\Lambda}}
+		  \sinh \left( \frac{\sqrt{3\Lambda}}{2}(\kappa+1) t \right)
+		  \right]^{2/3(\kappa+1)}   
+\end{equation}
+where $R_0$ is the scale factor of the universe (``radius'') at $t=0$;
+the density of energy reads
+\begin{equation}\label{dens}
+\epsilon(t)=\epsilon_0\,a(t)^{-3(\kappa+1)}\,.
+\end{equation}
+The stress-enegy tensor is one of a perfect fluid,
+\begin{equation}
+T_{\mu}^{\nu}=(\epsilon+p)u^{\nu}u_{\mu}-p \delta_{\mu}^{\nu}\,, 
+\end{equation}
+which depends on the covariant four-velocity  $u^{\mu}=dx^{\mu}/ds$
+(remember $p=\kappa \epsilon$).
 
-\verb|Exact::exactmodel = "Rob-Wal"| specifies a pure-radiation
-Robertson-Walker spacetime ($p = \frac{1}{3} \rho$, $k=0$), as described in
-Hawking and Ellis section~5.3 and MTW section~27.11 (see also gr-qc/0110031),
-transformed to the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates.
 The physics parameters are
-\begin{align}
-a &= \text{\tt Desitt\_a}						\\
-b &= \text{\tt Desitt\_b}						%%%\\
-\end{align}
-(note the names!).
+the equation of state parameter $\kappa = \verb|Lemaitre__kappa|$,
+the cosmological constant $\Lambda = \verb|Lemaitre__Lambda|$,
+the energy density of the universe at time $t = 0$,
+$\epsilon_0 = \verb|Lemaitre__epsilon0|$,
+and the scale factor (radius) of the universe at time $t = 0$,
+$R_0 = \verb|Lemaitre__R0|$.
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Robertson-Walker spacetime}
+\label{AEIThorns/Exact/sect-Robertson-Walker}
+
+\verb|Exact::exact_model = "Robertson-Walker"| specifies a 
+Robertson-Walker spacetime  as described in Hawking and Ellis section~5.3
+and MTW section~27.11 (see also gr-qc/0110031),
+transformed to the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates.
 The general Robertson-Walker line element in $(t,r,\theta,\phi)$ coordinates
 is
 \begin{equation}
 ds^2 = -dt^2 + R(t)^2 \left[ \frac{dr^2}{1 - kr^2} + r^2 \, d\Omega^2 \right]
 \end{equation}
 
-For the special case here, $R(t) = \sqrt{at}$, so
-\begin{equation}
-ds^2 = -dt^2 + a t \left[ dr^2 + r^2 \, d\Omega^2 \right]
-\end{equation}
-
-This thorn also sets up the stress-energy tensor for this spacetime.
-
-{\bf This solution doesn't work properly yet.  See Mitica Vulcanov for
-further information.}
+The physics parameters are
+the scale factor $R(t)$ at time $t = 0$, $R_0 = \verb|Robertson_Walker__R0|$,
+a parameter $\rho = \verb|Robertson_Walker__rho|$ which is related to
+the actual value of the matter density in the Universe,
+the geometry curvature parameter $k = \verb|Robertson_Walker__k|$,
+which can take (only) the values $k=-1$, $0$, or $+1$, corresponding
+to open, flat, or closed 3-geometries, and finally
+the Boolean parameter \verb|Robertson_Walker__pressure| to select
+whether or not to include pressure terms in the model.  If pressure
+is included we have a radiation-dominated universe $p = \frac{1}{3} \rho$;
+if pressure is not included we have a matter-dominated universe $p=0$.
+
+For a good simulation it is necessary to give good numerical values
+for the above parameters (they are very strictly related, through the
+Einstein equations).  See gr-qc/0110031 for some examples.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{De~Sitter Spacetime}
+\subsection{de~Sitter spacetime}
 
-\verb|Exact::exactmodel = "DeSitter"| specifies an Einstein-De~Sitter
+\verb|Exact::exact_model = "de Sitter"| specifies an Einstein-de~Sitter 
 spacetime (a zero-pressure spatially-flat Robertson-Walker spacetime),
 as described in Hawking and Ellis section~5.3 and MTW section~27.11
-(see also gr-qc/0110031), transformed to the usual Cactus $(t,x,y,z)$
-Cartesian-topology coordinates.  The physics parameters are
-\begin{align}
-a &= \text{\tt Desitt\_a}						\\
-b &= \text{\tt Desitt\_b}						%%%\\
-\end{align}
-(note the name!).
+(see also gr-qc/0110031 for some tests of Cactus with this model).
+The only physics parameter is the multiplicative scale
+factor $a = \verb|de_Sitter__scale|$.
 
 The Einstein-De~Sitter spacetime is the special case
 $R(t) = \sqrt{a}\,t^{2/3}$, $k = 0$ of the more general Robertson-Walker
@@ -509,36 +864,68 @@ The only non-vanishing component of the stress-energy tensor is
 \begin{equation}
 T_{tt} = \frac{1}{6 \pi t^2}
 \end{equation}
-This is properly set up by this thorn.
+This is properly set up by this thorn. 
 
-{\bf This solution doesn't work properly yet.  See Mitica Vulcanov for
-further information.}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{de~Sitter spacetime with cosmological constant}
+
+\verb|Exact::exact_model="de Sitter+Lambda"| specifies an Einstein-de~Sitter
+spacetime with a cosmological constant, with the line element
+\begin{equation}
+ds^2 = - dt^2 + e^{2/3\sqrt{3\Lambda}t} \left ( dx^2 + dy^2 + dz^2 \right) 
+\end{equation}
+where $\Lambda$ is the cosmological constant.
+FIXME: how is $\Lambda$ determined?
+
+The only physics parameter is the multiplicative scale
+factor $a = \verb|de_Sitter_Lambda__scale|$.
+
+The fictitious ``matter'' stress-energy tensor representing $\Lambda$ is
+\begin{equation}
+T_{ij}= - \frac{\Lambda}{8 \pi} g_{ij} = \left ( \begin{array}{cccc}
+\frac{1}{8}\frac{\Lambda}{\pi} & 0 & 0 & 0\\
+0 & -\frac{1}{8}\frac{\Lambda  e^{2/3 \sqrt{3\Lambda}t}}{\pi }& 0 & 0\\
+0 & 0 &-\frac{1}{8}\frac{\Lambda e^{2/3 \sqrt{3\Lambda}t}}{\pi }&  0\\
+0 & 0 & 0 & -\frac{1}{8}\frac{\Lambda  e^{2/3 
+\sqrt{3\Lambda}t}}{\pi}\end{array}\right ) \, 
+\end{equation}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{G\"{o}del Spacetime}
+\subsection{anti-de~Sitter spacetime with cosmological constant}
 
-\verb|Exact::exactmodel = "Godel"| (sic) specifies a G\"{o}del
-spacetime, as described in Hawking and Ellis section~5.7, transformed
-to the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates.  The
-only physics parameter is
+\verb|Exact::exact_model="anti-de Sitter+Lambda"| specifies an
+anti-de~Sitter spacetime with a cosmological constant, with the line
+element
 \begin{equation}
-a = \text{\tt Godel\_a}
+ds^2 =  dx^2 + e^{2/3\sqrt{-3\Lambda}t} \left ( -dt^2 + dy^2 + dz^2 \right)  
 \end{equation}
-(note the name!).
+FIXME: how is $\Lambda$ determined?
 
-At present this thorn doesn't set up the stress-energy tensor;
-you have to do this ``by hand''.
+The only physics parameter is the multiplicative scale
+factor $a = \verb|anti_de_Sitter_Lambda__scale|$.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Approximate Bianchi type~I spacetime}
+
+\verb|Exact::exact_model = "Bianchi I"| specifies an approximation to
+a Bianchi type~I spacetime, setting the spacetime metric components
+as harmonic functions. Thus this is not a proper solution of Einstein
+equations.  The only physics parameter is the multiplicative scale
+factor $a = \verb|Bianchi_I__scale|$.
 
 {\bf This solution doesn't work properly yet.  See Mitica Vulcanov for
 further information.}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Approximate Bianchi type~I Spacetime}
+\subsection{G\"{o}del spacetime}
 
-\verb|Exact::exactmodel = "BianchiI"| specifies an approximation to
-a Bianchi type~I spacetime.
+\verb|Exact::exact_model = "Goedel"| specifies a G\"{o}del spacetime,
+as described in Hawking and Ellis section~5.7.  The only physics parameter
+is the multiplicative scale factor $a = \verb|Goedel__scale|$.
 
 At present this thorn doesn't set up the stress-energy tensor;
 you have to do this ``by hand''.
@@ -548,54 +935,135 @@ further information.}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Kasner-like Spacetime}
+\subsection{Bertotti spacetime}
 
-\verb|Exact::exactmodel = "Kasner"| specifies a Kasner-like spacetime,
-as described in gr-qc/0110031, and in more detail in
-L. Pimentel,
-International Journal of Theoretical Physics {\bf 32}(6) [1993], 979,
-and
-S. Gotlober, {\it et.~al.\/},
-``Early Evolution of the Universe and Formation [of] Structure'',
-Akad. Verlag, 1990.
-There is one physics parameter,
+\verb|Exact::exact_model = "Bertotti"| specifies a Bertotti spacetime.
+This a spacetime metric with cosmological constant (see Gravitation
+and Geometry by Rindler and Trautman, Bibliopolis, Napoli, 1987,
+page~309), with the line element
 \begin{equation}
-q = \text{\tt Kasner\_q}						%%%\\
+ds^2 = -e^{2\sqrt{-\Lambda}x}dt^2 +dx^2 +  e^{2\sqrt{-\Lambda}z}du^2 + dz^2
 \end{equation}
+The only physics parameter is the cosmological constant
+$\Lambda = \verb|Bertotti__Lambda|$.
 
-In the usual Cactus $(t,x,y,z)$ Cartesian-topology coordinates, the
-4-metric is
+The fictitious ``matter'' stress-energy tensor representing $\Lambda$ is
 \begin{equation}
-g_{ab} = \text{diag}
-	 \left[
+T_{ij}= - \frac{\Lambda}{8 \pi} g_{ij} = \left ( \begin{array}{cccc}
+\frac{1}{8}\frac{\Lambda e^{2\sqrt{-\Lambda} x}}{\pi} & 0 & 0 & 0\\
+0 & -\frac{1}{8}\frac{\Lambda}{\pi }& 0 & 0\\
+0 & 0 &-\frac{1}{8}\frac{\Lambda e^{2\sqrt{-\Lambda}z}}{\pi }&  0\\
+0 & 0 & 0 & -\frac{1}{8}\frac{\Lambda}{\pi}\end{array}\right ) \, 
+\end{equation}
+
+Mitica Vulcanov says:
+This metric is not working properly. We suspect that it is not a solution
+of the vacuum Einstein equations with cosmological constant, thus
+somebody else can try to calculate properly the above components
+of the $T_{ij}$ - ask Mitica D.N. Vulcanov for more details.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{Kasner-like spacetime}
+
+\verb|Exact::exact_model="Kasner-like"| is the so-called
+``Kasner-like'' metric, as described in L.~Pimentel,
+Int.\ Journ.\ of Theor.\ Physics, {\bf 32},  No.~6, p.~979, (1993)
+and the references cited here.  (See also MTW section~30.2,
+gr-qc/0110031, and S.~Gotlober \etal{},
+``Early Evolution of the Universe and Formation [of] Structure'',
+Akad.\ Verlag, 1990.)
+The Kasner-like line element is
+\begin{equation}
+ds^2 = -dt^2 + t^{2q} (dx^2 +dy^2) + t^{2 - 4q}dz^2
+\end{equation}
+Here we have a stress-energy tensor which has all off-diagonal components 
+vanishing:
+\begin{eqnarray}
+T_{ij} = \left(
 	 \begin{array}{cccc}
-	 -1	& t^{2q}	& t^{2q} 	& t^{2-4q}	%%%\\
+	 q\frac{(2-3 q)}{8 \pi t^2} & 0 & 0 & 0 \\
+	 0 & q\frac{(2-3 q)t^{2q}}{8 \pi t^2} & 0 & 0\\
+	 0 & 0 & q\frac{(2-3 q)t^{2q}}{8 \pi t^2} & 0\\
+	 0 & 0 & 0 & q\frac{(2-3q)t^{2-4q}}{8 \pi t^2}%%%\\
 	 \end{array}
-	 \right]
+	 \right)
+\end{eqnarray}
+
+There is one parameter $q = \verb|Kasner_like__q|$.
+
+This metric forms a one parameter family of solutions of Einstein's
+equations with a perfect stiff fluid. The parameter $q$ is related to
+the energy density, as is obvious from the last equation. The
+qualitative features of the expansion depend on $q$ in the following
+way: for $q > 1/2$ the universe expands from a ``cigar'' singularity;
+for $q = 1/2$, the universe expands purely transversally from an
+initial ``barrel'' singularity; for $0 < q < 1/2$ the initial
+singularity is ``point-like'' and if $q \leq 0$ we have a ``pancake''
+singularity. The case $q=1/3$ corresponds to an isotropic universe
+with a stiff fluid; the case $q=0$ is a region of Minkowski spacetime
+in non-Cartesian coordinates. This family of metrics is ``Kasner-like''
+in the sense that the sum of the exponents is equal to one, but the
+sum of the squares is not equal to one except in the cases when $q=0$
+or $q=2/3$, when we have the vacuum case.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{axisymmetric Kasner spacetime}
+
+\verb|Exact::exact_model="Kasner-axisymmetric"| specifies an
+axisymmetric Kasner spacetime, as described in
+S.~D.~Hern, {\it Numerical Relativity and Inhomogeneous  Cosmologies\/},
+PhD thesis, Cambridge (gr-qc/0004036), and 
+S.~D.~Hern, J.~M.~Stewart, Class.\ Quantum Grav, {\bf 15}, 1581, (1998).
+The line element is
+\begin{equation}
+ds^2 = -\frac{dt^2}{\sqrt{t}} + \frac{dx^2}{\sqrt{t}} + t dy^2
++ t dz^2
 \end{equation}
-and the stress-energy tensor is
+This is an exact solution of the vacuum Einstein equations, explicitly
+homogeneous, and features a cosmological singularity at $t=0$.
+
+There are no parameters for this model.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\subsection{generalized Kasner spacetime}
+\verb|Exact::exact_model="Kasner-generalized"| specifies a
+generalized Kasner spacetime, as described in MTW section~30.2,
+where the line element is
 \begin{equation}
-T_{ab} = \text{diag}
-	 \left[
+ds^2 = -dt^2 +t^{2p_1}dx^2 + t^{2p_2}dy^2 + t^{2p_3}dz^2
+\end{equation}
+The Kasner parameters $p_1$, $p_2$ and $p_3$ must satisfy the relations
+$p_1+p_2+p_3 = 1$ and
+$p_1^2+p_2^2+p_3^2 = 1$.
+Restricting ourselves only to two parameters, $p_1$ and $p_2$,
+we have the following stress-energy tensor:
+\begin{equation}
+T_{ij} = \left(
 	 \begin{array}{cccc}
-	 q \displaystyle\frac{2 - 3q}{8\pi t^2}
-	     & q \displaystyle\frac{(2 - 3q) t^{2q}}{8\pi t^2}
-	         & q \displaystyle\frac{(2 - 3q) t^{2q}}{8\pi t^2}
-		     & q \displaystyle\frac{(2 - 3q) t^{2-4q}}{8\pi t^2}
-								%%%\\
+	 \frac{A}{8\pi t^2} & 0 & 0 & 0\\
+	 0 & \frac{A t^{2p_1-2}}{8 \pi} & 0 & 0\\
+	 0 & 0 & \frac{A t^{2p_2-2}}{8\pi} & 0 \\
+	 0 & 0 & 0 & \frac{A t^{-2p_1-2p_2}}{8 \pi}%%%
 	 \end{array}
-	 \right]
+	 \right)
 \end{equation}
+where $A = p_1 - p_1^2 +p_2 - p_2^2 - p_1 p_2$ (note the use of the above
+first condition on the parameters, thus we have $p_3 = 1-p_1-p_2$).  
 
-{\bf At the moment only $T_{00}$ is set properly, the other
-components are (incorrectly) 0.  See Mitica Vulcanov for
-further information.}
+The parameters are $p_1 = \verb|Kasner_generalized__p1|$
+and $p_2 = \verb|Kasner_generalized__p2|$.
+
+Mitica Vulcanov has done several simulations with various Kasner
+spacetimes, see gr-qc/0110031. 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Milne Spacetime for Pre-Big-Bang Cosmology}
 
-\verb|Exact::exactmodel = "Milne"| specifies a De~Milne spacetime,
+\verb|Exact::exact_model = "Milne"| specifies a Milne spacetime,
 as described by gr-qc/9802001 (see in particular reference~14, which
 in turn points to Zeldovich and Novikov volume~2 section~2.4):
 \begin{equation}
@@ -614,15 +1082,15 @@ V = \frac{t^2}{1 + x^2 + y^2 + z^2}
 \end{equation}
 
 {\bf The $g_{ab}$ given here is indeed what the code computes, but
-noone seems to know whether this is indeed a Milne (De~Milne?) spacetime.}
+alas noone seems to know whether this is indeed a Milne  spacetime.}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Miscellaneous Spacetimes}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsection{Boost-Rotation Symmetric Spacetime}
+\subsection{Boost Rotation Symmetric Spacetime}
 
 \verb|Exact::exactmodel = "starSchwarz"| specifies a boost-rotation
 symmetric spacetime.  Pravda and Pravdov\'{a}, gr-qc/0003067, give a
@@ -630,34 +1098,26 @@ general review of boost-rotation symmetric spacetimes.
 
 FIXME: get more info from Miguel and Carsten
 
+FIXME: the parameters are \dots
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Schwarzschild (Constant Density) Star}
 
-\verb|Exact::exactmodel = "starSchwarz"| specifies a constant-density
-``Schwarzschild'' star, as described in MTW~Box 23.2.  The stress-energy
-tensor is also properly set up.
+\verb|Exact::exact_model = "constant density star"| specifies a
+constant-density ``Schwarzschild'' star, as described in MTW~Box 23.2.
+The stress-energy tensor is also properly set up.
+
+The parameters are the star's mass \verb|constant_density_star__mass|
+and its radius \verb|constant_density_star__radius|.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \subsection{Non-Einstein Bowl (``Bag of Gold'') Spacetime}
 
-\verb|Exact::exactmodel = "bowl"| specifies a ``bag of Gold'' metric,
+\verb|Exact::exact_model = "bowl"| specifies a ``bag of Gold'' metric,
 as described in gr-qc/9809004.  This is useful for testing purposes,
-but isn't a solution of the Einstein equations.  The physics parameters
-are
-\begin{align}
-a	& = \text{\tt bowl\_a}						\\
-\sigma	& = \text{\tt bowl\_s}						\\
-c	& = \text{\tt bowl\_c}						\\
-\delta x& = \text{\tt bowl\_dx}						\\
-\delta y& = \text{\tt bowl\_dy}						\\
-\delta z& = \text{\tt bowl\_dz}						\\
-t_0	& = \text{\tt bowl\_t0}						\\
-\sigma_t& = \text{\tt bowl\_st}						%%%\\
-\end{align}
-There are also algorithm parameters \verb|bowl_type| and \verb|bowl_evolve|.
-
+but isn't a solution of the Einstein equations.
 The line element in $(t,r,\theta,\phi)$ coordinates is
 \begin{equation}
 ds^2 = -dt^2 + dr^2 + R^2(r) \, d\Omega^2
@@ -669,11 +1129,34 @@ and $\displaystyle \lim_{r \gg 1} R(r) = r$, so we have a flat 3-metric
 For intermediate values of~$r$, we take $0 < R(r) < r$; this deficit
 in areal radius produces the ``bag of gold'' geometry.
 
+The physics parameters are
+\begin{itemize}
+\item	$a = \verb|bowl__strength|$, the deformation strength
+\item	$c = \verb|bowl__center|$, the deformation center
+\item	\verb|bowl__shape| is a keyword parameter to specify
+	the type of function to use to specify the bowl (see below)
+\item	$\sigma = \verb|bowl__sigma|$, the deformation width
+	(\Nb{} for \verb|bowl__shape = "Gaussian"| the function
+	is actually $\exp \big( \!-(x-c)^2/\sigma^2 \big)$, not
+	$\exp \big( -\half(x-c)^2/\sigma^2 \big)$.  Thus for
+	this case $\sigma$ is actually $\sqrt{2}$ times the
+	standard deviation of the Gaussian.)
+\item	\verb|bowl__x_scale|, \verb|bowl__y_scale|, and \verb|bowl__z_scale|,
+	which set the $x$, $y,$ and $z$ scales of the bowl
+	(\ie{} all the computations actually use $x/\verb|bowl__x_scale|$,
+	$y/\verb|bowl__y_scale|$, and $z/\verb|bowl__z_scale|$)
+\item	\verb|bowl__evolve| is a Boolean parameter which controls
+	whether the bowl should be time-dependent; the remaining
+	parameters are only used if \verb|bowl__evolve| is true
+\item	$t_0 = \verb|bowl__t0|$, the center of the Fermi step in time
+\item	$\sigma_t = \verb|bowl__sigma_t|$, the width of the Fermi step in time
+\end{itemize}
+
 The size of the deviation from a flat geometry is controled by the
-parameter $a = \verb|bowl_a|$.  If $a = 0$, we are in flat spacetime.
-The width of the curved region is controled by $\sigma = \verb|bowl_s|$,
+parameter $a = \verb|bowl__strength|$.  If $a = 0$, we are in flat spacetime.
+The width of the curved region is controled by $\sigma = \verb|bowl__sigma|$,
 and the place where the curvature becomes significant (the center of
-the deformation) is controled by $c = \verb|bowl_c|$.
+the deformation) is controlled by $c = \verb|bowl__center|$.
 
 In detail, we choose
 \begin{equation}
@@ -688,44 +1171,47 @@ if \verb|bowl_evolve = "true"|.  For this latter case we have
 flat spacetime far in the past, and a static bowl far in the future.
 $f(r)$ is either a Gaussian or a Fermi function,
 \begin{equation}
-f(r) = \begin{cases}
-       \exp \left( -\frac{1}{2} (r-c)^2/\sigma^2 \right)
-			& \text{if {\tt bowl\_type = "Gauss"}}		\\[1ex]
+f(r) = \left\{
+       \begin{array}{ll}
+       \displaystyle
+       \exp \big( (r-c)^2/\sigma^2 \big)
+			& \hbox{if {\tt bowl\_type = "Gaussian"}}	\\[1ex]
        \displaystyle
        \frac{1}{1 + \exp(-\sigma(r-c))}
-			& \text{if {\tt bowl\_type = "Fermi"}}		%%%\\
-       \end{cases}
+			& \hbox{if {\tt bowl\_type = "Fermi"}}		%%%\\
+       \end{array}
+       \right.
 \end{equation}
-$g(r) = 1 - \text{sech}(4r)$ is a fixup factor to ensure that
+$g(r) = 1 - \sech 4r$ is a fixup factor to ensure that
 $\displaystyle \lim_{r \to 0} R(r) = r$.
 
-The three extra paramters $(\delta x, \delta y, \delta z)$
-scale the $(x,y,z)$ axes respectively.  Their default values are all~1.
-These parameters are useful to hide the spherical symmetry of the metric.
+The three paramters \verb|bowl__x_scale|, \verb|bowl__y_scale|, and
+\verb|bowl__z_scale| scale the $(x,y,z)$ axes respectively.  Their
+default values are all~1.  These parameters are useful to hide the
+spherical symmetry of the metric.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Acknowledgments}
 
-The original code, including the boostrot metric and the slice
-evolver, was written by C Gundlach and Miguel Alcubierre. Many
-different people have contributed exact solutions.  Jonathan Thornburg
-wrote most of this documentation in May 2002 based on the comments in
-the code, some reverse-engineering, and querying various people about
-how the code works.  The description of the Kastor-Traschen maximally
-charged multi-BH solutions is adapted from the file \verb|KTsol.tex|
-in this same directory, by Hisa-aki Shinkai.
+The original code, including the boost-rotation symmetric metric
+and the slice evolver, was written by Carsten Gundlach and Miguel Alcubierre.
+Many different people have contributed exact solutions.
+Mitica Vulcanov wrote the Schwarzschild/Lemaitre solution and most
+(all?) of the cosmological solutions.
+The Minkowski/gauge wave model was written by Michael Koppitz.
+In May-June 2002 Jonathan Thornburg cleaned up a lot of the code,
+systematized the spacetime/coordinate and parameter names, and
+wrote most of this documentation (based on the comments in the code,
+some reverse-engineering, and querying various people about how the
+code works.)
+The description of the Kastor-Traschen maximally charged multi-BH
+model is adapted from the file \verb|KTsol.tex| in this same directory,
+by Hisa-aki Shinkai.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-%
-% Automatically created from the ccl files 
-% Do not worry for now.
-%
-\include{interface}
-\include{param}
-\include{schedule}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Do not delete next line
+% END CACTUS THORNGUIDE
 
 \end{document}