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Diffstat (limited to 'doc/documentation.tex')
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1 files changed, 9 insertions, 18 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex index f6ca33d..5d8e7a8 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -82,7 +82,7 @@ associated parameters in turn. The Schwarzschild metric corresponds to a single, static, black hole. If the Cactus metric is specified as a conformal metric (by setting \texttt{admbase::metric\_type="yes"}), then the metric is -set using isotropic coordinates \cite{CactusEinstein_IDAnalytic_mtw-isotropic}: +set using isotropic coordinates \cite{CactusEinstein_IDAnalyticBH_mtw-isotropic}: \begin{equation} ds^2 = -\left(\frac{2r - M}{2r + M}\right)^2 + \left(1 + \frac{M}{2r}\right)^4 \left(dr^2 + r^2(d\theta^2 @@ -150,7 +150,7 @@ could modify your parameter file as follows: \section{Kerr} Kerr initial data for an isolated rotating black hole is specified -using the ``quasi-isotropic'' coordinates \cite{CactusEinstein_IDAnalytic_brandt-seidel:1996}: +using the ``quasi-isotropic'' coordinates \cite{CactusEinstein_IDAnalyticBH_brandt-seidel:1996}: \begin{equation} ds^2 = \psi^4 (dr^2 + r^2(d\theta^2 + \chi^2\sin^2\theta d\phi^2)), \end{equation} @@ -214,18 +214,15 @@ intial data with mass $M=1$ and angular momentum $a=0.3$ are: The earliest suggestion for initial data that might be said to corresponding to multiple black holes was given by Misner in 1960 -\cite{CactusEinstein_IDAnalytic_misner:1960}. He provided a prescription for writing a metric +\cite{CactusEinstein_IDAnalyticBH_misner:1960}. He provided a prescription for writing a metric connecting a pair of massive bodies, instaneously at rest, whose throats are connected by a wormhole. Using the method of images, this solution was generalised to describe any number of black holes whose throats connect two identical asymptotically flat spacetimes -\cite{CactusEinstein_IDAnalytic_misner:1963}. +\cite{CactusEinstein_IDAnalyticBH_misner:1963}. \begin{figure} \centering - \ifpdf - \else - \includegraphics[height=40mm]{misner.eps} - \fi + \includegraphics[height=40mm]{misner} \caption{The topology of the Misner spacetime is that of a pair of asymptotically flat sheets connected by a number of Einstein-Rosen bridges. By construction, an exact isometry exists between the upper @@ -254,7 +251,7 @@ where the conformal factor $\psi$ is given by \end{equation} The extrinsic curvature for the Misner data is zero. -The parameter $\mu_0$ is a measure of the ration of mass to separation +The parameter $\mu_0$ is a measure of the ratio of mass to separation of the throats, and is set using the parameter \texttt{idanalyticbh::mu}. For values less than $\mu\simeq 1.8$, the throats will have a single event horizon. @@ -306,10 +303,7 @@ the first black hole lies on the $x$-axis (as in Figure \begin{figure} \centering \label{fig:multi_misner} - \ifpdf - \else - \includegraphics[height=40mm]{multi_misner.eps} - \fi + \includegraphics[height=40mm]{multi_misner} \caption{Configuration for three Misner throats using the \texttt{multiple\_misner\_bh} initial data.} \end{figure} @@ -347,13 +341,10 @@ data which differs from the Misner data mainly in its choice of spacetime topology. Whereas the Misner data presumes that the throats connect a pair of asymptotically flat spacetimes which are identical to each other, the Brill-Lindquist data connects each throat to a -separate asymptotically flat region \cite{CactusEinstein_IDAnalytic_brill-lindquist:1963}. +separate asymptotically flat region \cite{CactusEinstein_IDAnalyticBH_brill-lindquist:1963}. \begin{figure} \centering - \ifpdf - \else - \includegraphics[height=40mm]{brill_lindquist.eps} - \fi + \includegraphics[height=40mm]{brill_lindquist} \caption{Two Brill-Lindquist throats connecting separate asymptotically flat regions.} \end{figure} |