From 688f28aadbc49af93730288e4d71256e447fc295 Mon Sep 17 00:00:00 2001 From: knarf Date: Mon, 7 May 2012 14:56:33 +0000 Subject: some initial documentation git-svn-id: http://svn.aei.mpg.de/numrel/AEIThorns/ADMMass/trunk@45 54511f98-0e4f-0410-826e-eb8b393f5a1e --- doc/documentation.tex | 169 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 169 insertions(+) create mode 100644 doc/documentation.tex (limited to 'doc/documentation.tex') diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..33c6dd8 --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,169 @@ +% *======================================================================* +% 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 +% relevant 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 +% % START 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 separated with a \\ or a comma. +% - You can define your own macros, but they must appear after +% the START CACTUS THORNGUIDE line, and must 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 graphicx package. +% More specifically, with the "\includegraphics" command. Do +% not specify any graphic file extensions in your .tex file. This +% will allow us 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{...} +% - Do not use \appendix, instead include any appendices you need as +% standard sections. +% - 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} + +% 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/latex/cactus} + +\begin{document} + +% The author of the documentation +\author{Frank Löffler} + +% The title of the document (not necessarily the name of the Thorn) +\title{ADMMass} + +% the date your document was last changed, if your document is in CVS, +% please use: +% \date{$ $Date: 2004-01-07 14:12:39 -0600 (Wed, 07 Jan 2004) $ $} +\date{2012-05-07} + +\maketitle + +% Do not delete next line +% START CACTUS THORNGUIDE + +% Add all definitions used in this documentation here +% \def\mydef etc + +% Add an abstract for this thorn's documentation +\begin{abstract} +Thorn ADMMass can compute the ADM mass from quantities in ADMBase. +\end{abstract} + +% The following sections are suggestive only. +% Remove them or add your own. + +\section{Introduction} +The ADM mass evaluated as either surface integrals at infinity or volume +integrals over entire hypersurfaces give a measure of the total energy in the +spacetime. + + The ADM mass can be defined~\cite{Omurchadha74} as a surface integral over a + sphere with infinite radius: + \begin{equation} + \label{eq:ADM_mass} + M_{\mbox{\tiny ADM}}=\frac{1}{16\pi}\oint_\infty + \sqrt{\gamma}\gamma^{ij}\gamma^{kl} + (\gamma_{ik,j}-\gamma_{ij,k})\textrm{d}\! S_l + \end{equation}. + This is, assuming $\alpha=1$ at infinity, equivalent to + \begin{equation} + \label{eq:ADM_mass_volume} + M_{\mbox{\tiny ADM}}=\frac{1}{16\pi}\int + \left(\alpha\sqrt{\gamma}\gamma^{ij}\gamma^{kl} + (\gamma_{ik,j}-\gamma_{ij,k})\right)_{,l}\textrm{d}\!^{\,3}\!\!x + \end{equation}. +In practice, the following equation can also be used within the thorn: + \begin{equation} + \label{eq:ADM_mass_lapse} + M_{\mbox{\tiny ADM}}=\frac{1}{16\pi}\oint_\infty + \alpha\sqrt{\gamma}\gamma^{ij}\gamma^{kl} + (\gamma_{ik,j}-\gamma_{ij,k})\textrm{d}\! S_l. + \end{equation} + This differs from equation~(\ref{eq:ADM_mass}) by the factor $\alpha$ inside + the integral. For evaluations of those equations at infinity, $\alpha=1$ is + assumed, and they are equal. For evaluations at a finite distance, however, + this is usually not the case and the approximation of the ADM mass is + gauge-dependent~\cite{Omurchadha74}. Depending on circumstances, + either~(\ref{eq:ADM_mass}),~(\ref{eq:ADM_mass_lapse} or~~(\ref{eq:ADM_mass_volume}) + might give better results. + +\section{Using This Thorn} + +\subsection{Basic Usage} + + + +\subsection{Special Behaviour} + +\subsection{Interaction With Other Thorns} + +\subsection{Examples} + +\subsection{Support and Feedback} + +\section{History} + +\subsection{Thorn Source Code} + +\subsection{Thorn Documentation} + +\subsection{Acknowledgements} + + +% Do not delete next line +% END CACTUS THORNGUIDE + +\end{document} -- cgit v1.2.3