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\documentstyle{report}
\newcommand{\parameter}[1]{{\it #1}}
\begin{document}
\chapter{IDAnalyticBH}
\begin{tabular}{@{}ll}
Code Authors & Joan Masso, Paul Walker, Ed Seidel. Gabrielle Allen \\
Maintained by & Cactus Developers \\
Documentation Authors &
\end{tabular}
\section{Introduction}
\subsection{Purpose of Thorn}
Thorn IDAnalyticBH provides analytic initial data for vacuum black
hole spacetimes. Initial data is provided for the 3-metric, extrinsic
curvature, and if appropriate the conformal factor and it's spatial
derivatives. The current initial data sets are for a single (Schwarzschild)
black hole in isotropic coordinates, up to four Brill-Lindquist black
holes, and any number of Misner-type black holes.
\subsection{Technical Specification}
\begin{itemize}
\item{Implements} einsteinID
\item{Inherits from} einstein
\item{Tested with thorns} Einstein
\end{itemize}
\section{Theoretical Background}
\section{Algorithmic and Implementation Details}
This thorn uses no special numerical methods, however two points
are worth noting
\begin{enumerate}
\item{} The solution for Misner is obtained by summing a sequence
\item{} The spatial derivatives of the conformal metric (when required)
are calculated accurately using finite differencing of the
exact solution by a very small spacing
\end{enumerate}
\section{Using the Thorn}
This thorn can provide either the physical metric (use\_conformal=''no'')
or the conformal metric and a conformal factor (and its spatial derivatives)
(use\_conformal=''yes''). In general, the option use\_conformal=''yes'' should
be used, since ????.
\section{Parameters}
\subsection{Extended Parameters}
\begin{tabular}{l|l|l|l}
&&&\\
einstein &&&\\
\hline
\parameter{initial\_data} & KEYWORD & schwarzschild & One Schwarzschild black hole \\
& & bl\_bh & Brill Lindquist black holes \\
& & misner\_bh &Misner black holes \\
& & multiple\_misner\_bh & Multiple Misner black holes \\
\parameter{initial_lapse} & KEYWORD & schwarz & Set lapse to schwarzschild \\
\end{tabular}
\subsection{Private Parameters}
\begin{tabular}{l|l|l|l|l}
&&&&\\
Schwarzschild & & & & \\
\hline
\parameter{mass} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 2.0 & Mass of black hole \\
&&&&\\
Multiple Misner & & & & \\
\hline
\parameter{mu} & {\t CCTK\_REAL} & $[0,\infty)$ & 1.2 & Misner $\mu$ value \\
\parameter{nmax} & {\t CCTK\_INT} & $[0,\infty)$ & 30 & Numer of terns to include for Misner series \\
\parameter{misner\_nmh} & {\t CCTK\_INT} & $[0,10]$ & 1 & Number of Misner black holes \\
&&&&\\
Brill Lindquist & & & & \\
\hline
\parameter{bl\_nbh} & {\t CCTK\_INT} & $[1,4]$ & 1 & Number of Brill Lindquist black holes\\
\parameter{bl\_x0\_1} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & x-position of first BL hole\\
\parameter{bl\_y0\_1} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & y-position of first BL hole\\
\parameter{bl\_z0\_1} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & z-position of first BL hole\\
\parameter{bl\_M\_1} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 1.0 & mass of first BL hole\\
\parameter{bl\_x0\_2} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & x-position of second BL hole\\
\parameter{bl\_y0\_2} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & y-position of second BL hole\\
\parameter{bl\_z0\_2} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & z-position of second BL hole\\
\parameter{bl\_M\_2} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 1.0 & mass of second BL hole\\
\parameter{bl\_x0\_3} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & x-position of third BL hole\\
\parameter{bl\_y0\_3} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & y-position of third BL hole\\
\parameter{bl\_z0\_3} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & z-position of third BL hole\\
\parameter{bl\_M\_3} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 1.0 & mass of third BL hole\\
\parameter{bl\_x0\_4} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & x-position of fourth BL hole\\
\parameter{bl\_y0\_4} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & y-position of fourth BL hole\\
\parameter{bl\_z0\_4} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 0.0 & z-position of fourth BL hole\\
\parameter{bl\_M\_4} & {\t CCTK\_REAL} & $(-\infty,\infty)$ & 1.0 & mass of fourth BL hole\\
\end{tabular}
\subsection{Discussion}
\section{Interaction with Other Thorns}
It is still to be decided how initial data should be supplied to
for systems of evolution equations which use more or different
variables to those in the einstein implementation
\section{Future Development}
Initial data sets which are missing from this thorn include
\begin{itemize}
\item{} Boosted single black hole
\item{} Single black hole in harmonic spatial coordinates
\item{} Single black hole in Eddington-Finkelstein coordinates
\end{itemize}
\end{document}
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